The object of the present paper is to find a necessary and sufficient condition for an invariant submanifold of an LP -Sasakian manifold to be totally geodesic. An illustrative example is given to support the obtained result.

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On Invariant Submanifolds of LP-Sasakian Manifolds

Semi-Invariant Submanifolds

CR-submanifolds of nearly hyperbolic Sasakian manifold with a semi-symmetric metric connection are studied. We obtain horizontal and vertical CR- submanifolds of a nearly hyperbolic Sasakian manifold with a semi-symmetric metric connection. Parallel distributions on CR-submanifolds of nearly hyperbolic Sasakian manifold with semi-symmetric metric connection are calculated.

CR-submanifolds of a nearly hyperbolic Sasakian manifold with a semi-symmetric metric connection

On semi-invariant submanifolds of a nearly Sasakian manifold with a quarter symmetric non-metric connection

We consider a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric metric connection and study semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semi-symmetric metric connection. We also find the integrability conditions of some distributions on nearly hyperbolic Kenmotsu manifold andstudy parallel distributions on nearly hyperbolic Kenmotsu manifold.

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On Semi-Invariant Submanifolds of a Nearly Hyperbolic Kenmotsu Manifold with Semi-symmetric Metric Connection

We consider a Kenmotsu manifold immersed in  almost $r$-contact manifold admitting a quarter- symmetric non-metric connection and study semi-invariant submanifolds of an almost $r$-contact  Kenmotsu manifold immersed in almost $r$-contact Riemannian manifold endowed with a quarter- symmetric non- metric connection. We also discuss the integrability conditions of distribution on Kenmotsu manifold.

Semi-invariant submanifolds of Kenmotsu manifold immersed in a generalized almost r-contact structure admitting quarter-symmetric non-metric connection

In this paper, $CR$-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection are studied. The parallel distributions relating to $\xi$-vertical and $\xi$-horizontal $CR$-submanifolds of nearly trans-hyperbolic Sasakian manifold with a semi symmetric non-metric connection are obtained. Moreover, Nijenhuis tensor is calculated and integrability conditions of the distributions on $CR$ submanifolds of nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection are discussed.

/pdf/cr-submanifolds-of-a-nearly-trans-hyperbolic-sasakian-zas0ufge5h.pdf

$CR$-Submanifolds of a Nearly Trans-Hyperbolic Sasakian Manifold with a Semi-Symmetric Non-Metric Connection

In this paper, generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection are studied. Moreover, integrability conditions of the distributions on generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection and geometry of leaves with semi-symmetric non-metric connection have been discussed. 2000 Mathematical Subject Classification :53C21, 53C25, 53C05.

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Janardan Parsad Ojha

Papers

Semi-invariant submanifolds of Kenmotsu manifold immersed in a generalized almost r-contact structure admitting quarter-symmetric non-metric connection

$CR$-Submanifolds of a Nearly Trans-Hyperbolic Sasakian Manifold with a Semi-Symmetric Non-Metric Connection

Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection