Semi-invariant $ξ^{\bot}$-submanifolds of generalized quasi-Sasakian manifolds

Details Semi-invariant $ξ^{\bot}$-submanifolds of generalized quasi-Sasakian manifolds Semi-invariant $ξ^{\bot}$-submanifolds of generalized quasi-Sasakian manifolds

2010-05-03

arxiv.org/abs/1005.0184v1

Mathematics

Differential Geometry

Dedicated to the memory of Prof. Stere Ianus (1939-2010)

Scientific paper

A structure on an almost contact metric manifold is defined as a generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic. Then we consider a semi-invariant $\xi^{\bot}$-submanifold of a manifold endowed with such a structure and two topics are studied: the integrability of distributions defined by this submanifold and characterizations for the totally umbilical case. In particular we recover results of Kenmotsu, Eum and Papaghiuc.

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