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Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion

Part of the Lecture Notes in Mathematics book series (LNM,volume 1156)

Keywords

  • Fundamental Form
  • Isometric Immersion
  • Integral Manifold
  • Sasakian Manifold
  • Riemannian Submersion

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References

  1. Bourbaki, N.: Variétés différentielles et analytiques, Fascicule de resultats. Paris: Hermann 1971

    MATH  Google Scholar 

  2. Blair, D.E.: Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics, Vol. 509; Berlin, Heidelberg, New York: Springer(1976; Zbl. 319.53026).

    MATH  Google Scholar 

  3. Backes, E., Reckziegel, H.: On symmetric submanifolds of spaces of constant curvature. Math.Ann.263,419–433(1983; Zbl. 499.53045).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Chen, B.Y.: Geometry of submanifolds. New York: Marcel Decker (1973; Zbl. 262.53036).

    MATH  Google Scholar 

  5. Chen, B.Y., Houh, C.S.: Totally real submanifolds of a quaternion projective space. Ann.di Mat.(IV)120,185–199(1979; Zbl. 413.53031).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Chen, B.Y., Ogiue, K.: On totally real submanifolds. Trans.of Amer.Math.Soc.193,257–266(1974; Zbl. 286.53019).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Dieudonné, J.: Treatise on analysis, Vol. IV. New York,London: Academic Press (1974; Zbl. 292.58001).

    MATH  Google Scholar 

  8. Ehresmann,C.: Les connexions infinitésimales dans un espace fibré différentiable. Colloque de Topologie, Bruxelles 1950, 29–55

    Google Scholar 

  9. Ferus, D.: Symmetric submanifolds of euclidean space. Math. Ann.247,81–93(1980; Zbl. 446.53041).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Hermann, R.: A sufficient condition that a mapping of Riemannian manifolds be a fibre bundle. Proc.Amer.Math.Soc.11,236–242 (1960; Zbl. 112,137).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Ishihara, S.: Quaternion Kählerian manifolds and fibred Riemannian spaces with Sasakian 3-structure. Kōdai Math.Sem. Rep.25,321–329(1973; Zbl. 267.53023).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Ishihara, S.: Quaternion Kählerian manifolds. J.Diff.Geometry 9,483–500(1974; Zbl. 297.53014).

    MathSciNet  MATH  Google Scholar 

  13. Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. I. New York: Interscience Publishers 1963

    MATH  Google Scholar 

  14. Lawson, H.B.: Rigidity theorems in rank-1 symmetric spaces. J.Diff.Geometry 4,349–357(1970; Zbl. 199,564).

    MathSciNet  MATH  Google Scholar 

  15. Morimoto, A.: On normal almost contact structures with a regularity. Tôhoku Math.J.16,90–104(1964; Zbl. 135,221).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Naitoh, H.: Parallel submanifolds of complex space forms. Nagoya Math.J.90,85–117(1983) and 91,119–149(1983; Zbl. 502.53044/5).

    MathSciNet  MATH  Google Scholar 

  17. O'Neill, B.: The fundamental equations of a submersion. Michigan Math.J.13,459–469(1966; Zbl. 145,186).

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. O'Neill, B.: Semi-Riemannian geometry. New York: Academic Press (1983; Zbl. 531.53051).

    MATH  Google Scholar 

  19. Wu, H.: On the de Rham decomposition theorem. Illinois J.Math. 8,291–311(1964; Zbl. 122,400).

    MathSciNet  MATH  Google Scholar 

  20. Yano, K. Kon, M.: Anti-invariant submanifolds. New York: Marcel Decker (1976; Zbl. 349.53055).

    MATH  Google Scholar 

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© 1985 Springer-Verlag

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Reckziegel, H. (1985). Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075098

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  • DOI: https://doi.org/10.1007/BFb0075098

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  • Print ISBN: 978-3-540-15994-0

  • Online ISBN: 978-3-540-39698-7

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