Siberian Mathematical Journal

, Volume 26, Issue 1, pp 133–147 | Cite as

Geometric properties of immersed manifolds

  • S. Z. Shefel'


Geometric Property 
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Literature Cited

  1. 1.
    J. Nash, “Problem of immersion for Riemannian manifolds,” Usp. Mat. Nauk,26, No. 4, 173–216 (1971).Google Scholar
  2. 2.
    H. Weyl, “Definition of a closed convex surface by its line elements,” Usp. Mat. Nauk,3, No. 2, 159–190 (1948).Google Scholar
  3. 3.
    A. D. Aleksandrov, Intrinsic Geometry of Convex Surfaces, [in Russian], Gostekhizdat, Moscow-Leningrad (1948).Google Scholar
  4. 4.
    A. V. Pogorelov, Extrinsic Geometry of Convex surfaces [in Russian], Nauka, Moscow (1969).Google Scholar
  5. 5.
    N. V. Efimov, “Origin of singularities on surfaces of negative curvature,” Mat. Sb.,64, No. 2, 286–320 (1964).Google Scholar
  6. 6.
    S. Z. Shefel', “Surfaces in Euclidean space,” in: Mathematical Analysis and Adjacent Questions of Mathematics [in Russian], Nauka, Novosibirsk (1978), pp. 297–318.Google Scholar
  7. 7.
    S. Z. Shefel', “Completely regular isometric immersions in Euclidean space,” Sib. Mat. Zh.,11, No. 2, 442–460 (1970).Google Scholar
  8. 8.
    S. Z. Shefel', “C1-smooth isometric immersions,” Sib. Mat. Zh.,15, No. 6, 772–793 (1974).Google Scholar
  9. 9.
    G. S. Shefel', “Geometric properties of groups of transformations of Euclidean space,” Dokl. Akad. Nauk SSSR,277, No. 4, 803–806 (1984).Google Scholar
  10. 10.
    S. Z. Shefel', “Two classes of k-dimensional surfaces in n-dimensional space,” Sib. Mat. Zh.,10, No. 2, 459–466 (1969).Google Scholar
  11. 11.
    Yu. E. Borovskii and S. Z. Shefel', “A theorem of Chern-Kuijper,” Sib. Mat. Zh.,19, No. 6, 1386–1387 (1978).Google Scholar
  12. 12.
    V. V. Glazyrin, “Topological and metric properties of k-saddle surfaces,” Dokl. Akad. Nauk SSSR,233, No. 6, 1028–1030 (1977).Google Scholar
  13. 13.
    A. A. Borisenko, “Extrinsic geometric properties of parabolic surfaces and topological properties of saddle surfaces in symmetric spaces of rank one,” Mat. Sb.,116, No. 3, 440–457 (1981).Google Scholar
  14. 14.
    A. A. Borisenko, “Cylindricity of complete parabolic surfaces in Euclidean space,” in: Symposium on Geometry in the Large and the Foundations of Relativity Theory. Abstracts of Reports [in Russian], Novosibirsk (1982), pp. 11–12.Google Scholar
  15. 15.
    A. A. Borisenko, “Multidimensional parabolic surfaces in Euclidean space,” Ukr. Geom. Sb., No. 25, 3–5 (1982).Google Scholar
  16. 16.
    V. V. Glazyrin, “Riemannian curvature of multidimensional saddle surfaces,” Sib. Mat. Zh.,19, No. 3, 555–563 (1978).Google Scholar
  17. 17.
    N. A. Rozenson, “Riemannian surfaces of class I,” Izv. Akad. Nauk SSSR, Ser. Mat.,4, No. 2, 181–192 (1940); 5, Nos. 4–5, 325–352 (1940);7, Nos. 2–6, 253–284 (1943).Google Scholar
  18. 18.
    H. Jacobowitz, “Implicit function theorems and isometric embeddings,” Ann. Math.,95, No. 2, 191–225 (1972).Google Scholar
  19. 19.
    I. Kh. Sabitov and S. Z. Shefel', “Connections between orders of smoothness of a surface and its metric,” Sb. Mat. Zh.,17, No. 4, 916–925 (1976).Google Scholar
  20. 20.
    S. Z. Shefel', “Conformal correspondence of metrics and smoothness of isometric immersions,” Sib. Mat. Zh.,20, No. 2, 397–401 (1979).Google Scholar
  21. 21.
    Yu. G. Reshetnyak, “Differential properties of quasiconformal mappings and conformal mappings of Riemannian spaces,” Sib. Mat. Zh.,19, 1166–1184 (1978).Google Scholar
  22. 22.
    S. Z. Shefel', “Smoothness of a conformal mapping of Riemannian spaces,” Sib. Mat. Zh.,23, No. 1, 153–159 (1982).Google Scholar
  23. 23.
    A. V. Pogorelov, “Regularity of convex hypersurfaces with regular metric,” Dokl. Akad. Nauk SSSR,224, No. 1, 39–42 (1975).Google Scholar
  24. 24.
    S. Z. Shefel', “Questions of the geometry of immersions of manifolds,” in: Symposium on Geometry in the Large and Foundations of the Theory of Relativity. Abstracts of Reports [in Russian], Novosibirsk (1982), pp. 117–118.Google Scholar
  25. 25.
    F. Klein, Comparative Survey of the Latest Geometric Investigations. Foundations of Geometry [Russian translation], Gostekhizdat, Moscow (1956).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

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  • S. Z. Shefel'

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