Contact totally umbilical submanifolds of a sasakian space form
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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.
KeywordsComplex Space Fundamental Form Space Form Complex Space Form Sasakian Space Form
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