TRANSVERSAL HYPERSURFACES OF ALMOST HYPERBOLIC CONTACT MANIFOLDS WITH A QUARTER SYMMETRIC NON METRIC CONNECTION

TRANSVERSAL HYPERSURFACES OF ALMOST HYPERBOLIC CONTACT MANIFOLDS WITH A QUARTER SYMMETRIC NON METRIC CONNECTION

Shamsur Rahman    

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Abstract

Transversal hypersurfaces of trans hyperbolic contact manifolds endowed with a quarter symmetric non metric connection are studied. It is proved that transversal hypersurfaces of almost hyperbolic contact manifold with a quarter symmetric non metric connection admits an almost product structure and each transversal hypersurfaces of almost hyperbolic contact metric manifold with a quarter symmetric non metric connection admits an almost product semi-Riemannian structure. The fundamental 2- form on the transversal hypersurfaces of cosymplectic hyperbolic manifold and ( ; 0) trans hyberbolic Sasakian manifold with hyperbolic (f; g; u; v; )-structure are closed. It is also proved that transversal hypersurfaces of trans hyperbolic contact manifold with a quarter symmetric non metric connection admits a product structure. Some properties of transversal hypersurfaces with a quarter symmetric non metric connection are proved.

Keywords

Hypersurfaces, Quarter Symmetric semi-metric connection, Quasi-sasakian manifold, Gass and Weingarten equations.