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arXiv · 1510.06774

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

S. K. Srivastava·A. Sharma
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Abstract

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

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S. K. Srivastava, A. Sharma. 2015-10-28. Geometry of $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifolds in paracosymplectic manifold. https://doi.org/10.1007/s00022-016-0325-3

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