The purpose of this paper is to study PR-semi-invariant warped product submanifolds of a paracosymplectic manifold M . We prove that the distributions associated with the definition of PR-semi-invariant warped product submanifold M are always integrable. A necessary and sufficient condition for an isometrically immersed PR-semi-invariant submanifold of M to be a PR-semi-invariant warped product submanifold is obtained in terms of the shape operator.Mathematics Subject Classification (2010). 53B25, 53B30, 53C25, 53D15.
The present article deals with the study of PR-pseudo-slant warped product submanifolds of paracosymplectic manifols M. Results of non-existence for non-trivial PR-pseudo-slant warped product submanifolds with proper slant coefficient in M are shown. In addition to these results, we give an elementary illustration of non-trivial PR-pseudo-slant warped product submanifold with improper slant coefficient in M .
A generalized Chen-type inequality and corresponding equality consequences for sequential warped products are proved in this paper. These results, which are based on such warped products having factors holomorphic, totally real and pointwise slant, extend Chen-type inequality for various warped products on nearly Kähler manifolds. Moreover, we also examine the related special cases.
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