The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.
The object of the present paper is to study weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds. It is shown that weakly -symmetric and weakly -Ricci symmetric Kenmotsu manifolds are -Einstein.
We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudo-slant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold...
The object of the present paper is to study -Ricci solitons on -Einstein -manifolds. It is shown that if is a recurrent torse forming -Ricci soliton on an -Einstein -manifold then is (i) concurrent and (ii) Killing vector field.
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