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Differential geometric structures on differentiable manifolds

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Abstract

In this paper we present a study of differential geometric structures arising on manifolds imbedded in almost complex spaces and the differential geometry of such manifolds.

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Literature cited

  1. D. V. Beklemishev, “The differential geometry of a space with almost complex structure,” in: Geometry. 1963 [in Russian], Itogi Nauki VINITI AN SSSR, Moscow (1965), pp. 165–212.

    Google Scholar 

  2. R. Zulanke and P. Vintgen, Differential Geometry and Bundles [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  3. G. F. Laptev, “Differential geometry of immersed manifolds. Group-theoretic method of differential geometric investigations,” Tr. Mosk. Mat. O-va, No. 2, 275–382 (1953).

    Google Scholar 

  4. G. F. Laptev, “On the invariant equipment of a surface in a space with affine connection,” Dokl. Akad. Nauk SSSR,126, No. 3, 490–493 (1959).

    Google Scholar 

  5. G. F. Laptev, “On the equipment of a surface in a space with affine connection,” Lit. Mat. Sb.,3, No. 2, 212 (1963).

    Google Scholar 

  6. G. F. Laptev, “Manifolds immersed in a generalized space,” in: Proceedings of the Fourth All-Union Mathematical Congress, 1961 [in Russian], Vol. 2, Nauka, Leningrad (1964), pp. 226–233.

    Google Scholar 

  7. G. F. Laptev, “Basic infinitesimal structures of higher order on smooth manifolds,” Tr. Geometr. Sem. Inst. Nauchn. Inf., Akad. Nauk SSSR,1, 139–189 (1966).

    Google Scholar 

  8. G. F. Laptev, “On an invariant analytic theory of differentiable maps,” Tr. Geometr. Sem. Inst. Nauchn. Inf., Akad. Nauk SSSR,6, 37–42 (1974).

    Google Scholar 

  9. G. F. Laptev and N. M. Ostianu, “On pairs of distributions in manifolds with almost complex structure,” in: Fifth All-Union Conference on Contemporary Problems of Geometry. Thesis Reports [in Russian], Samarkand (1972), p. 113.

  10. G. F. Laptev and N. M. Ostianu, “(f, ξ, η, ρ)-structures on differentiable manifolds,” Itogi Nauki Tekh. VINITI Akad. Nauk SSSR, Probl. Geometr.,7, 5–22 (1975).

    Google Scholar 

  11. N. M. Ostianu, “On submanifolds of spaces with, a)-structure,” in: Third Baltic Geometry Conference, Thesis Reports [in Russian], Palanga (1968), pp. 119–121.

  12. N. M. Ostianu, “On some projective-differential structures on differentiable manifolds,” Tr. Geometr. Semin. Inst. Nauchn. Inf., Akad. Nauk SSSR,2, 207–246 (1969).

    Google Scholar 

  13. N. M. Ostianu, “Distributions of m-dimensional linear elements in a space with connection, II,” Tr. Geometr. Semin. Inst. Nauchn. Inf.,Akad. Nauk SSSR,3, 95–114 (1971).

    Google Scholar 

  14. N. M. Ostianu, Differential Geometric Structures on Fiber Spaces [in Russian], VINITI AN SSSR, Moscow (1973).

    Google Scholar 

  15. N. M. Ostianu, “Piecewise fibered spaces,” Tr. Geometr. Semin. Inst. Nauchn. Inf., Akad. Nauk SSSR,5, 259–309 (1974).

    Google Scholar 

  16. N. M. Ostianu, “Distributions of pairs of linear elements in equipped fibered spaces with Hp-structure,” Tr. Semin. Kafedry Geometr. Kazan. Univ., No. 8, 72–84 (1975).

    Google Scholar 

  17. N. M. Ostianu, “Differential geometric structures on multidimensional surfaces in an almost complex space,” in: Sixth All-Union Conference on Contemporary Problems in Geometry. Thesis Reports [in Russian], Vilnius State Inst., Vilnius (1975).

    Google Scholar 

  18. N. M. Ostianu, “On a class of (fξηρ)-structures,” in: Fourth Republican Conference on Mathematics. Belorussii, “Problems in the development of applied mathematical studies”; Thesis Reports [in Russian], Minsk (1975).

  19. N. M. Ostianu, “Differential geometric structures induced by an (fξηρ)-structure on surfaces in an almost complex space,” in: Thesis Reports. All-Union Scientific Conference on Non-Euclidean Geometry “150 Years of Lobachevskian Geometry” [in Russian], Kazan (1976), p. 154.

  20. N. M. Ostianu, V. V. Ryzhkov, and P. I. Shveikin, “Sketch of the scientific studies of G. F. Laptev,” Tr. Geometr.Semin.Inst. Nauchn. Inf., Akad. Nauk SSSR, 47–70 (1973).

  21. N. D. Polyakov, “Differential geometric structures on almost contact manifolds,” in: Problems of Geometry [in Russian], Vol. 8, Itogi Naukl i Tekhn. VINITI AN SSSR (1976), pp. 114–139.

  22. S. Sternberg, Lectures on Differential Geometry [Russian translation], Mir, Moscow (1970).

    Google Scholar 

  23. A. P. Shirokov, “Structures on differentiable manifolds,” in: Algebra. Topology. Geometry. 1967 [in Russian], Itogi Nauki VINITI AN SSSR, Moscow (1969), pp. 127–188.

    Google Scholar 

  24. A. P. Shirokov, “Structures on differentiable manifolds,” in: Algebra. Topology. Geometry [in Russian], Vol. 11, Itogi Nauki i Tekhniki VINITI AN SSSR (1974), pp. 153–207.

  25. D. E. Blair, G. D. Ladden, and M. Okumura, “Hypersurface of an even-dimensional sphere satisfying a certain commutative condition,” J, Math. Soc. Jpn.,25, No. 2, 202–210 (1973).

    Google Scholar 

  26. D. E. Blair, G. D. Ladden, and K. Yano, “Induced structures on submanifolds,” Kodai Math. Sem. Reports,22, No. 2, 188–198 (1970).

    Google Scholar 

  27. D. E. Blair, G. D. Ladden, and K. Yano, “Geometry of complex manifolds similar to the CalabiEckmann manifolds,” J. Diff. Geometry,9, No. 2, 263–274 (1974).

    Google Scholar 

  28. D. E. Blair, G. D. Ladden, and K. Yano, “Semi-invariant immersions,” Kodai Math. Sem. Reports,27, No. 3, 313–319 (1976).

    Google Scholar 

  29. U-hang Ki, Jin Suk Pak, and Hyun Bae Suh, “On (fgu(k)α(k))-structures,” Kodai Math. Sem. Reports,26, Nos. 2–3, 160–175 (1975).

    Google Scholar 

  30. Masahiro Kon, “On some complex submanifolds in Kaehler manifolds,” Can. J. Mathi,26, No. 6, 1442–1449 (1974).

    Google Scholar 

  31. G. D. Ladden and M. Okumura, “Some integral formulas and their applications to hypersurfaces of Sn Λ Sn,” J. Diff. Geometry,9, No. 4, 618–631 (1974).

    Google Scholar 

  32. R. S. Millman, “f-Structures with parallelizable kernel on manifolds,” J. Diff. Geometry,9, No. 4, 531–535 (1974).

    Google Scholar 

  33. Masafumi Okumura, “Certain hypersurfaces of an odd dimensional sphere,” Tohoku Math. J.,19, No. 4, 381–395 (1967).

    Google Scholar 

  34. B. B. Sinha and I. J. P. Singh, “Generalised (f, g, u, v, λ)-structure,” Proc. Indian Acad.,A81, No. 1, 1–8 (1975).

    Google Scholar 

  35. Kichiro Takamatsu and Hong-Suh Park, “Certain hypersurfaces of a manifold with (f, g, u, v, λ)-structure,” Kanadzava Daigaku Kogakubu Kie, Mem. Fac. Technol. Kanazawa Univ.,7, No. 2, 1–7 (1973).

    Google Scholar 

  36. Yoshiko Watanabe, “Totally umbilical surfaces in normal contact Riemannian manifolds,” Kodai Math. Sem. Reports,19, No. 4, 474–487 (1967).

    Google Scholar 

  37. Seuchi Yamaguchi, “On hypersurfaces in Sasakian manifolds,” Kodai Math. Sem. Reports,21, No. 1, 64–72 (1969).

    Google Scholar 

  38. Seuchi Yamaguchi, “Remarks on a totally real submanifold,” Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis., Mat., Natur.,57, Nos. 3–4, 177–180 (1974) (1975).

    Google Scholar 

  39. Seuchi Yamaguchi and Toshihiko Ikawa, “Remarks on a totally real submanifold,” Proc. Jpn. Akad.,51, No. 1, 5–6 (1975).

    Google Scholar 

  40. Kentaro Yano and Masafumi Okumura, “Invariant hypersurfaces of a manifold with (f, g, u, v, λ)-structure,” Kodai Math. Sem. Reports,23, No. 3, 290–304 (1971).

    Google Scholar 

  41. Kentaro Yano and Masafumi Okumura, “Invariant submanifolds of a manifold with (f, g, u, v, λ)-structure,” Kodai Math. Sem. Reports,24, No. 1, 75–90 (1972).

    Google Scholar 

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Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 8, pp. 89–111, 1977.

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Ostianu, N.M. Differential geometric structures on differentiable manifolds. J Math Sci 13, 600–613 (1980). https://doi.org/10.1007/BF01091818

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