Non-existence of PR-pseudo-slant warped product submanifolds of paracosymplectic manifolds

Abstract

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 .

Pointwise PR-pseudo slant submanifolds of para-Kähler manifolds

“…From Eqs. (17) and (18), we obtain that D ⊥ and D λ are the subspaces spanned by span{Z 1 , Z 2 } and span{Z 3 , Z 4 } respectively, where D ⊥ is a totally real distribution and D λ is a pointwise slant distribution with slant function λ = cos(v). Thus, M becomes a proper pointwise PR-pseudo-slant submanifold of M .…”

“…Srivastava and the author continued the study for paracosymplectic manifolds [20]. Recently Alegre-Carriazo [1,2] and Srivastava-Sharma [17,18] carried out the notion for slant, semi-slant, pseudo slant submanifolds in para geometries particularly in para-Hermitian and paracosymplectic manifolds, and presented analogies and differences between structure admitted semi-Riemannian and Riemannian metrics.…”