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: partially supported through the UGC-BSR Start-Up-Grant vide their Letter No. F.30-29/2014(BSR). A. Sharma: supported by Central University of Himachal Pradesh through the Research fellowship for Ph.D.
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Srivastava, S.K., Sharma, A. Geometry of \({\mathcal{P}\mathcal{R}}\)-semi-invariant warped product submanifolds in paracosymplectic manifold. J. Geom. 108, 61–74 (2017). https://doi.org/10.1007/s00022-016-0325-3
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DOI: https://doi.org/10.1007/s00022-016-0325-3