ON AN INVARIANT SUBMANIFOLD OF HYPERBOLIC SASAKIAN MANIFOLDS

Shravan Kumar Pandey, Ram Nawal Singh

DOI Number
10.22190/FUMI1703353P
First page
353
Last page
367

Abstract


The object of the present paper is to study an invariant submanifold of hyperbolic Sasakian maifolds. In this paper, we consider semiparallel and 2-semiparallel invariant submanifolds of hyperbolic Sasakian manifold and it is shown that these submanifolds are totally geodesic. It is also proved that on an invariant submanifold of hyperbolic Sasakian manifolds the conditions $I(X, Y).\alpha = 0$, $I(X, Y).\tilde{\nabla}\alpha = 0$, $C(X, Y).\alpha = 0$, $C(X, Y).\tilde{nabla}\alpha = 0$ holds if and only if it is totally geodesic.

Keywords

hyperbolic Sasakian manifold, invariant submanifold, semiparallel submanifold, 2-semiparallel submanifold, totally geodesic submanifold

Keywords


hyperbolic Sasakian manifold, invariant submanifold, semiparallel submanifold, 2-semiparallel submanifold, totally geodesic submanifold

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References


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