Publications by Vladimir Rovenski

 

  • PhD and Doctoral Dissertations
    1. Multi-dimensional uniquely projecting surfaces in a sphere and projective spaces. Ph.D., 109 pp., 1984, Institute of Mathematics, Novosibirsk, Russia, scientific advisor Prof. V. Toponogov
    2. Geometry and topology of foliations with nonnegative curvature in mixed directions. Doctoral Dissertation, 224 pp., 1994, Institute of Mathematics, Novosibirsk, Russia, scientific consultant Prof. V. Toponogov.
  • Books
    1. Beta-spline method for curves and surfaces modeling. State Pedagogical University at Krasnoyarsk, text-book, 1992, 51 pp. (Russian)
    2. Theory of curves (Appendix: Curves on display with DERIVE). State Pedagogical University at Krasnoyarsk, text-book, 1996, 196 pp. (Russian)
    3. Geometry of Surfaces with MAPLE. State Pedagogical University at Krasnoyarsk, text-book, 1997, 104 pp. (Russian)
    4. Foliations on Riemannian Manifolds and Submanifolds. Birkhauser, USA, 1998, 286 pp. (English)
    5. On the yacht MAPLE on waves of curves. State Pedagogical University at Krasnoyarsk, text-book, 1998, 128 pp. (Russian)
    6. Foliations, submanifolds and mixed curvature. Collection of surveys: "Itogi Nauki & Tehniki. Geometry", VINITI (Moscow), 1999, 109 p.,
      English translation: J. Math. Sci, New York, 99, No.6, 1699-1787 (2000)
    7. Geometry of Curves and Surfaces with MAPLE, 2000, 310 pp., Boston, MA, Birkhauser, USA (English)
    8. Analytical Methods in Anisotropic Elasticity with Symbolic Computational Tools, 2005, 451 pp., Birkhauser, USA (English), commonly with O.Rand (Technion)
    9. Editorial assistance and translation (from Russian) of the textbook by V.A.Toponogov
      “Differential Geometry of Curves and Surfaces: A Concise Guide”. Birkhauser Boston, USA, 174 pp., 2005.
  • Articles in Refereed Journals
    1. Quasi-affine functions. Optimizacija, 1976, v.18 (35), 107–111
    2. Totally geodesic foliations. Siberian Math. Journal, 1982, v. 23 (1), 217–219
    3. Ruled surfaces in a sphere. Siberian Math. Journal, 1984, v. 25 (6), 945–955
    4. Quasi-developing and parabolic submanifolds in a sphere. Soviet Math. Doklady, 1984, v.30,  373–375
    5. Local curvature properties of Hopf fibrations, 1–17. Deposited by VINITI with Siberian Math. Journal, No. 5909, Moscow, 8 July 1985
    6. Decomposition of ruled and parabolic surfaces. Soviet Math. Doklady, 1989, v. 39 (2), 366–368
    7. Uniform Riemannian manifolds admitting periodic functions. Siberian Math. Journal, v. 30 (1), 1989, 156–159
    8. Characterization of totally geodesic submanifolds of Sn and CPn. Journal Soviet Math., 1990, v. 48 (1),  87–94
    9. Remarks on complete parabolic surfaces. Journal Soviet Math., 1990, v. 51 (5),  2565–2566
    10. The metric structure of ruled and parabolic surfaces in Sn and CPn. Siberian Math. Journal, 1990, v. 30 (5), 783–793
    11. Skew Hopf fibrations. Journal of Math. Sciences, 1991, v. 53 (5), p. 532–541 (Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 101–104, 1990)
    12. Totally geodesic foliations with an orthogonal distribution that is close to integrable. Siberian Math. Journal, 1991, v. 32 (1), 161–165.
    13. Conditions for the decomposition of ruled and parabolic surfaces in S n and CP n. Journal Soviet Math. 1992, v. 59 (2), 763–770.
    14. Totally geodesic foliations, close to Riemannian ones. Journal Math. Sciences, New York, 1994, v. 72 (4), 3234–3236.
    15. Geodesic foliations with positive mixed sectional curvature. Math. Physics, Analysis and Geometry, Kharkov, 1994, v. 1(2), 232–239.
    16. Metric decomposition of foliations with nonnegative curvature. Russian Academy Science Doklady, Math., 1994, v. 49, 202–205.
    17. Classes of submersions of Riemannian manifolds with compact leaves. Siberian Math. Journal, 1994, v. 35 (5), 1027–1035.
    18. A local theorem on distributions whose mixed sectional curvature is positive. Russian Math. (Izv. VUZ), 1994, v. 38 (4), 27–29.
    19. Foliations with nonnegative mixed sectional curvature. 42 pp. Deposited by VINITI through Siberian Math. Journal, No. 2130-B94, Moscow, 31 August 1994
    20. Decomposition of foliations and ruled submanifolds with nonnegative mixed curvature. Russian Math. (Izv. VUZ), v. 39 (7), 1995, 35–47.
    21. Distributions and compact foliations with nonnegative mixed sectional curvature. Izv. VUZ, Mat., 1998, 18 pp.
    22. Foliations on closed geodesics with positive mixed sectional curvature and special behaviour of L-Jacobi fields. Collection: "Proc. of Geometrical Seminar", v. 23, Kazan, 1998, 113–123
    23. On the role of partial Ricci curvature in Geometry of Submanifolds and foliations. Ann. Polonici Math., v. LXVIII.1, 1998,  61–82.
    24. Partial Ricci curvature of a submanifold inside a cylinder or cone of Euclidean space. Siberian Math. Journal, 1998, v. 39 (6), 1195–1202.
    25. Analysis of Anisotropic Beams – An Analytic Approach, Journal of Applied Mechanics, v. 68(4), 2001, 674–678 (with O. Rand)
    26. Positiveness of mixed curvature and dimension of foliation, Zesz. Nauk. Uniw. Jagiell., Univ. Iagell. Acta Math. 2000, 1245(38), 67–88.
    27. Non-Homogeneous Uncoupled Beam Under Tip Loads. Science and Engineering of Composite Materials, 12 (4), 2005, 229–240. (with O. Rand et al)
    28. Non-Homogeneous Uncoupled Beam Under Axially Distributed Loads. Science and Engineering of Composite Materials, 12 (4), 2005, 241–250. (with O. Rand et al)
    29. Level Based Formulation for Beams of Generic Anisotropy. Science and Engineering of Composite Materials, 13 (1), 2006, 37–54. (with O. Rand)
    30. Kelvin-Helmholtz Instability Model for Supersonic Viscid Jet. Int. J. of Pure & Applied Math., 24(4), 2005, 537–551 (with Gaissinski I.M.)
    31. Conformal nullity of isotropic submanifolds. Annales Polonici Mathematici, v. 86.1, 2005, 47–57.
    32. On (k, ε)-saddle submanifolds of Riemannian manifolds. Geometry and Dedicata. 121, 2006, 187–203.
    33. About topology of saddle submanifolds. Journal of Differential Geometry and Its Applications. 25(2) 2007, 220–233. (with A. Borisenko)
    34. The test for adequacy of shell models for a turbulence problem. Int. J. of Pure & Applied Math., 36(4), 2007, 407–418 (with Gaissinski I.M.)
    35. Submanifolds with restrictions on extrinsic q-th scalar curvature. Israel Journal of Mathematics, 159, 2007, 289–316.
    36. Saint-Venant's Problem for Homogeneous Piezoelectric Beams, J. Applied Mech., 2007, 74 (6), 1095–1103 (with Harash E. & Abramovich H.)
    37. Behavior of Piezoelectric Beams under Axially Non-Uniform Distributed Loading. J. Elasticity, 2007, 88 (3), 223–253 (with Abramovich H.)
    38. Kelvin-Helmholtz Instability Model for a Supersonic Adiabatic Jet. Int. J. of Pure & Applied Math., 44(4), 2008, 235–248 (with Gaissinski I.M. and Kelis O.)
    39. Saint-Venant’s Problem for Compound Piezoelectric Beams. J. Elasticity, 2009, 96, 105–127 (with Abramovich H.)
    40. Some extensions of the class of k-convex bodies, Siberian Math. J., 50 (5) 2009, 820–829 (with V.P. Golubyatnikov).
    41. Integral formulae on foliated symmetric spaces. Math. Annalen. To be published, 2008, 21 pp. (with P. Walczak)

  • Articles or Chapters in Books which are not Conference Proceedings
    1. On mathematical support of investigations of multi-phase systems using data of thermal analysis, p. 93–127. Collection: “Multi-Component Systems”, Proceedings of Institute of Geology and Geophysics at Novosibirsk, Science, 1977
    2. On mathematical support of investigations of multi-phase systems, 80–92. Collection: “Multi-Component Physical-Chemical Systems”, Proceedings of Institute of Geology and Geophysics at Novosibirsk, Science, 1980
    3. On quantitative description of multi-phase systems using data of thermal analysis, 73–77. Collection: “Multi-Phase Physical-Chemical Systems”, Proceedings of Institute of Geology and Geophysics at Novosibirsk, Science, 1980
    4. Algebraic characterization of complex projective space with Fubini metric, 77–85. Collection: “Differential equations and applications”, State University of Alma-Ata, 1984, 133 pp.
    5. Structure of totally real parabolic surfaces in complex and quaternion projective spaces. Deposited by KazNIITI in Alma-Ata, preprint No. 831 Ka-D94, 8 January 1985, 13 pp.
    6. Geodesic foliations on the three-dimensional sphere. 115–119. Collection: ‘‘Theoretical and applied problems in differential equations”, State University of Karaganda, 1986, 131 pp.
    7. Geometric characteristics of a complex projective space, 98–104, (with V. Toponogov) Coll. ‘‘Geometry and topology of homogeneous spaces”, Altaiskii State University, Barnaul, 1988
    8. Pseudo-Riemannian ruled and parabolic submanifolds, 54–66. Collection: ‘‘Geometry of multi-dimensional spaces”, Altaiskii State University, Barnaul, 1991
    9. Theorem on totally geodesic foliations with positive mixed sectional curvature and its applications. 50–58. Coll. ‘‘Geometry of multi-dimensional spaces”, Altaiskii State University, Barnaul, 1994
    10. Submanifolds and foliations with restrictions on partial Ricci curvature, 53–62. Collection: ‘‘Problems of Mathematical Analysis”, Technical University of Krasnoyarsk, 1996
    11. Teaching geometry of curves using DERIVE, 7–11. The Bulletin of DERIVE + TI-92 User Group, No. 28, 1997
  • Articles in Conference Proceedings
    1. Foliations on closed geodesics with positive mixed sectional curvature, 25–26. Proceedings of 5th Siberian Workshop ‘‘Algebra and Analysis”, Irkutsk, 1993
    2. The integral of mixed scalar curvature along a leaf of foliation, 93–102. Proceedings 6th Intern. Conference ‘‘Differential Geometry and Applications", Masaryk University, Brno, 1996
    3. Great sphere foliations and manifolds with curvature bounded above. Commonly with V. Toponogov, 1996, preprint, dg-ga/9609007, 13 pp.
    4. Submanifolds with restrictions on q-Ricci curvature, 375–388. Proceedings International Conference ‘‘Differential Geometry”, Budapest, 1998
    5. Geometry in Pedagogical University basing on Computer Algebra Systems, 255–260. Proceedings 3rd Inter-Karelian Conference ‘‘Teaching Mathematics and Physics in Secondary and Higher education”, Petrozavodsk, 1998
    6. Analysis of Laminated Composite Beams - An Analytic Approach, 467–478. Proceedings of the 40th Israel Annual Conference on Aerospace Sciences, February 2000, Haifa, p. 467–478 (with O. Rand)
    7. A Closed-Form Solution for Laminated Composite Beams, # 00015, Proceedings of the American Helicopter Society 56th Annual Forum, Virginia Beach, Virginia, 2000 (with O. Rand)
    8. A Closed-Form Solution for Elastic Equilibrium of Laminated Composite Beams, p. 15. Proceedings of the Annual Meeting of the Israel Mathematical Union, 2000, Haifa (with O. Rand)
    9. Analysis of the Elastic Coupling in Laminated Composite Beams, 57-59. Proceedings of the 28th Israel Conference on Mechanical Engineering, June 2000, Beer-Sheva (with O. Rand)

10.        Elastic Coupling and Interlaminar Phenomena in Laminated Composite Beams, # 00062. Proc. of the American Helicopter Society 57th  Annual Forum, Washington, DC, 2001 (with O. Rand)

11.        Analysis of Anisotropic Beams with Axially Non-uniform Stress Distribution, Proc. of the 41st Israel Annual Conference on Aerospace Sciences, 2001, Haifa, 369–379 (with O. Rand)

12.        Polynomial Solutions for Problems in Anisotropic Elasticity with Symbolic Computational Tools, Proceedings of the 42nd Israel Annual Conference on Aerospace Sciences, 2002, Tel-Aviv–Haifa, 28 pp. (with O. Rand)

13.        Analytical Approach to Composite Beam Analysis, Proceedings of 23rd Congress of the International Council of the Aeronautical Sciences (ICAS), Toronto, Canada,  2002 (with O. Rand)

14.        Non-Homogeneous Composite Beams Under Tip Loading, Proceedings of the American Helicopter Society 59th Annual Forum, Arizona, 6-8 May, 2003 (with O. Rand)

15.        Non-Homogeneous Composite Beams, Proceedings of 24th Congress of the International Council of the Aeronautical Sciences (ICAS), Iokohama, Japan, 2004 (with O. Rand)

16.        On topology of saddle submanifolds. International Conference ‘’Differential Geometry and Applications’’, 29 Aug. – 2 Sept. 2005, Budapest, Hungary.

17.        Integral formulae for foliations on Riemannian manifolds, Proc. of the 10-th International Conf. on DGA2007, Olomouc, August 27–31, 2007, 193–204, World Scientific, 2008 (with P. Walczak).

18.        Variational formulae for the total mean curvatures of a codimension-one distribution, Proc. of the 8-th International Colloquium, Santiago-de Compostela, Spain, July 7–11, 2008, 83–93, World Scientific, 2009 (with P. Walczak). 

  • Other Scientific Publications
    1. On Riemannian submersions with totally geodesic fibers, 170–171. Regional Conference of young scientists. Theses, Karaganda, 1983 (Russian)
    2. Geometrical characterization of complex projective space, p. 132. 8th Russian Conference on Modern Problems of Differential Geometry”. Theses, Odessa, 1984
    3. Automation subsystem of quality control of rubber-technical mixtures using micro computer”, Industry of synthetic rubbers, tires and rubber products, vol. 7, 1985, 37-38
    4. Periodical functions on Riemannian Manifolds, p. 109. Russian Workshop on Optimal Control, Geometry and Analysis. Theses, Kemerovo, 1986
    5. Geometric characteristics of a Complex Projective Space, 95–96. Notes of Moscow State University, series “Mathematics”, theses, 1986, No. 5 (with V. Toponogov)
    6. Geometrical characterizations of a Complex Projective Space, p. 102. Russian Conference on Differential Geometry “in the Large”. Theses, Novosibirsk, 1987, 146 pp.
    7. Metrical structure of Ruled Surfaces in the Sphere, p. 103. Russian Conference on Differential Geometry “in the Large”. Theses, Novosibirsk, 1987, 146 pp.
    8. Pseudo-Riemannian Ruled Submanifolds, 267-268. 9th Russian Conference on Modern Geometry. Theses, Kishinev, 1988
    9. Applying of Computer Graphics for Modeling in Archeology, p. 122. Conference “Computer Graphics-89”. Theses, Novosibirsk, 1989 (with Rudkowski N., etc.)

10.        Totally geodesic foliations with an orthogonal distribution that is close to integrable, p. 68. International Conference on Geometry and Analysis. Theses, Novosibirsk, 1989

11.        Curvature and topology of manifold with totally geodesic distribution, p.74. International Conference in memory A. Shirshov. Theses, Barnaul, 1991

12.        Diameter of leaves and dimension of foliation with positive mixed sectional curvature, p. 84. International Science Conference “Lobachevskii and modern physics”, Theses, Kazan, 1992

13.        Training space and creative imagination of students in geometry courses using computer technologies, p. 63. Regional Conference: "Humanity and democracy of training process in Pedagogical Universities", Theses, Krasnoyarsk, 1992 (commonly with O. Odintsova and V. Mayer)

14.        Using new information technologies in training teachers of mathematics, informatica and drawing, p. 163. Proceedings Russian Seminar: "Problems of training teachers of mathematics in Pedagogical Universities", Theses, Lipetsk, 1993 (with O. Odintsova)

15.        Distributions with positive mixed sectional curvature, p. 84. International Geometrical Seminar in memory of P. Shirokov, Theses, Kazan, 1995

16.        The integral of mixed scalar curvature along a leaf of foliation, p. 100. Proceedings 6th Intern. Conference "Diff. Geometry and Applications", Masaryk University, Brno, Theses, 1996

17.        Submanifolds and foliations with restrictions on partial Ricci curvature, 79–80. Proceedings 2nd Siberian Congress on Applied Mathematics (INPRIM-96), Theses, Novosibirsk, 1996

18.        Teaching Differential Geometry with DERIVE, p. 122–123. Proceedings 2nd Siberian Geometrical Conference, Theses, Tomsk, 1996, 144 pp.

19.        Foliations on Riemannian manifolds and Submanifolds, p. 71. Proceedings 2nd Siberian Geometrical Conference, Theses, Tomsk, 1996, 144 pp.

20.        Foliations on closed geodesics with positive mixed sectional curvature and special behaviour of L-Jacobi fields, p. 139. International Geometrical Seminar “Modern Geometry and Theory of Physical Fields”, Theses, Kazan, 1997

21.        Practical works on differential geometry with DERIVE + MAPLE in Pedagogical University, p. 53–54. International Conference “New Information Technologies in University Education”, Theses, Novosibirsk, 1997, 210 p.

1.            Geometrical training in Pedagogical University on base of Computer Algebra Systems, p. 53–54. International Conference “New Information Technologies in University Education”, Theses, Novosibirsk, 1998, 220 p.

2.            Foliations, Submanifolds and mixed Curvature, p. 80. Proceedings 3rd Siberian Congress on Applied Mathematics (INPRIM-98), Theses, Novosibirsk, 1998

3.            Analytical Methods in Anisotropic Elasticity (with Maple symbolic tools), Proceedings of the Annual Meeting of the Israel Mathematical Union, 7 June 2001, Weizmann Institute, Rehovot (with O. Rand)

4.            Formulation and Analytic Solution for Laminated Beams, p. 8. 5th Theoretical Day of Composite Materials and Structures, 15 May 2001, Haifa, Technion (with O. Rand) 

5.            Non-Homogeneous Composite Beams Under Tip Loading, p. 8. 6th Theoretical Day of Composite Materials and Structures, 30 June 2003, Haifa, Technion (with O. Rand)

6.            On topology of saddle submanifolds. (To memory of Prof. V. Toponogov), p. 15. The Annual Meeting of IMU, 19-20 May 2005, Neve Ilan.

7.            Anisotropic Beam Analysis with Symbolic Computational Tools. Proc. 2nd Int. Conference of Applied Mathematics, 12–17 Aug. 2005, Plovdiv, Bulgaria.

8.            On topology of saddle submanifolds. Int. Conf. ‘’Diff. Geometry and Applications’’, 29 Aug.–2 Sept. 2005, Budapest, Hungary.

9.            Kelvin-Helmholtz Instability Model for Supersonic Viscid Jet. Third Int. Conf. on Complex Analysis & Dynamical Systems, January 2–6, 2006, Galilee, Israel. (with Gaissinski I.M.)

10.        Almansi-Michell Problem for Homogeneous Piezoelectric Beams, TAE Report, No. 969, 108 pp, 2006, Technion – Israel Institute of Technology (with Abramovich H.)

11.        Integral formulae on foliated symmetric spaces (with P. Walczak, Poland), The Annual Meeting of the IMU, 25-26 May 2006, Neve Ilan.

12.        Saint-Venant's Problem for Homogeneous Piezoelectric Beams, TAE Report, No. 975, 90 pp, 2007, Technion – Israel Institute of Technology (with Harash E. and Abramovich H.)

13.        Some extensions of the class of convex bodies, Math.DG, arXiv: 0808.1788, 2008, 18 pp. (with V.P. Golubyatnikov)

14.        Some extensions of the class of k-convex bodies, Math.DG, arXiv: 0809.3643, 2008, 13 pp. (with V.P. Golubyatnikov)