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


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.


Complex Space Fundamental Form Space Form Complex Space Form Sasakian Space Form 
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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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