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2014•Mathematical Sciences and Applications E-NotesOpen access

HYPERSURFACES SATISFYING SOME CURVATURE CONDITIONS ON PSEUDO PROJECTIVE CURVATURE TENSOR IN THE SEMI-EUCLIDEAN SPACE

Yusuf Doğru

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Abstract

We consider some curvature conditions on the Pseudo projectivecurvature tensor P on a hypersurface in the semi-Euclidean space En+1. Wes prove that every pseudo projectively Ricci-semisymmetric hypersurface M satisfying the condition P · R = 0 is pseudosymmetric. We also consider thecondition P · S = 0 on hypersurfaces of the semi-Euclidean space En+1.s

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We consider some curvature conditions on the Pseudo projectivecurvature tensor P on a hypersurface in the semi-Euclidean space En+1. Wes prove that every pseudo projectively Ricci-semisymmetric hypersurface M satisfying the condition P · R = 0 is pseudosymmetric. We also consider thecondition P · S = 0 on hypersurfaces of the semi-Euclidean space En+1.s

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Available abstract

We consider some curvature conditions on the Pseudo projectivecurvature tensor P on a hypersurface in the semi-Euclidean space En+1. Wes prove that every pseudo projectively Ricci-semisymmetric hypersurface M satisfying the condition P · R = 0 is pseudosymmetric. We also consider thecondition P · S = 0 on hypersurfaces of the semi-Euclidean space En+1.s

Key concepts: Hypersurface, Mathematics, Riemann curvature tensor, Curvature, Euclidean space, Ricci curvature, Euclidean geometry, Pure mathematics

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