The Journal of the Indian Mathematical Society

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On Semiparallel and Weyl-Semiparallel LP-Sasakian Hypersurfeces of Kaehler Manifolds


Affiliations
1 Department of Mathematics, D. D. U. Gorakhpur University, Gorakhpur, India
2 Department of Mathematics, Alwar Institute of Engineering and Technology, Alwar, 301030, India
     

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In this paper we studied semiparallel and Weyl-semi- parallel an LP-Sasakian hypersurfaces of Kaehler manifolds. We investi- gated that an LP-Sasakian hypersurfaces of a Kaehler manifold is semi- parallel if it is totally umbilical with negative unit mean curvature and the necessary condition for an LP-Sasakian hypersurfaces of Kaehler mani- folds is pseudo parallel if LH=1. Further such a hypersurface is Weyl- semiparallel if and only if it is Eta-Einstein manifold. We also studied the Quasi-umbilical hypersurfaces of an LP-Sasakian manifold and obtain several results.

Keywords

LP-Sasakian Manifolds, Kaehler Manifold, Semiparellel, Weyl-Semiparallel and Quasi-Umbilical Hypersurfaces.
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  • On Semiparallel and Weyl-Semiparallel LP-Sasakian Hypersurfeces of Kaehler Manifolds

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Authors

Dhruwa Narain
Department of Mathematics, D. D. U. Gorakhpur University, Gorakhpur, India
Sunil Yadav
Department of Mathematics, Alwar Institute of Engineering and Technology, Alwar, 301030, India
Ajai Srivastava
Department of Mathematics, D. D. U. Gorakhpur University, Gorakhpur, India

Abstract


In this paper we studied semiparallel and Weyl-semi- parallel an LP-Sasakian hypersurfaces of Kaehler manifolds. We investi- gated that an LP-Sasakian hypersurfaces of a Kaehler manifold is semi- parallel if it is totally umbilical with negative unit mean curvature and the necessary condition for an LP-Sasakian hypersurfaces of Kaehler mani- folds is pseudo parallel if LH=1. Further such a hypersurface is Weyl- semiparallel if and only if it is Eta-Einstein manifold. We also studied the Quasi-umbilical hypersurfaces of an LP-Sasakian manifold and obtain several results.

Keywords


LP-Sasakian Manifolds, Kaehler Manifold, Semiparellel, Weyl-Semiparallel and Quasi-Umbilical Hypersurfaces.