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Annali di Matematica Pura ed Applicata

, Volume 114, Issue 1, pp 351–364 | Cite as

Contact totally umbilical submanifolds of a sasakian space form

  • Ikuo Ishihara
  • Masahiro Kon
Article

Summary

We define a notion of contact totally umbilical submanifolds of Sasakian space forms corresponds to those of totally umbilical submanifolds of complex space forms. We study a contact totally umbilical submanifold M of a Sasakian space form\(\overline M \left( c \right)\) (c ≠ −3) and prove that M is an invariant submanifold or an anti-invariant submanifold. Furthermore we study a submanifold M with parallel second fundamental form of a Sasakian space form\(\overline M \left( c \right)\) (c ≠ 1) and prove that M is invariant or anti-invariant.

Keywords

Complex Space Fundamental Form Space Form Complex Space Form Sasakian Space Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • Ikuo Ishihara
    • 1
  • Masahiro Kon
    • 1
  1. 1.Tokyo

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