Geometry of $\mathcal{PR}$-semi-invariant warped product submanifolds in paracosymplectic manifold

Abstract

The purpose of this paper is to study $\mathcal{PR}$-semi-invariant warped product submanifolds of a paracosymplectic manifold $\tilde{M}$. We prove that the distributions associated with the definition of $\mathcal{PR}$-semi-invariant warped product submanifold $M$ are always integrable. A necessary and sufficient condition for an isometrically immersed $\mathcal{PR}$-semi-invariant submanifold of $\tilde{M}$ to be a $\mathcal{PR}$-semi-invariant warped product submanifold is obtained in terms of the shape operator.

15 pages. arXiv admin note: text overlap with arXiv:1510.02044

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• A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds
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Cited by in corpus (1)

• Geometry of pointwise pseudo-slant warped product submanifolds in a Kähler manifold