Geometric inequalities of PR-warped product submanifold in para-Kenmotsu manifold

Abstract

The main purpose of this paper is to study the properties of PR-semi-invariant submanifold of para-Kenmotsu manifold. We obtain the integrability conditions for the invariant distribution and anti-invariant distribution. We obtain some existence and non-existence results of PR-semi-invariant warped product submanifolds. We provide some necessary and sufficient conditions for PR-semi-invariant submanifold to be a PR-semi-invariant warped product submanifold in para-Kenmotsu manifold. We also derive some sharp inequalities for PR-semi-invariant warped product submanifold in para-Kenmotsu manifolds.

Keywords

• para contact manifold
• submanifold
• warped product