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

TL;DR

This paper studies semi-invariant $\xi^{ot}$-submanifolds within generalized quasi-Sasakian manifolds, focusing on integrability conditions and characterizations of totally umbilical cases, extending known results in contact geometry.

Contribution

It introduces a new class of submanifolds in generalized quasi-Sasakian manifolds and provides new integrability and umbilicality conditions, generalizing previous results.

Findings

Conditions for integrability of distributions

Characterizations of totally umbilical submanifolds

Extension of Kenmotsu, Eum, and Papaghiuc results

Abstract

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.