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2023•Journal of Applied Mathematics and PhysicsOpen access

Inequalities for Scalar Curvature and Shape Operator of an R-Lightlike Submanifold in Semi-Riemannian Manifold

Ménédore Karimumuryango, Domitien Ndayirukiye, Hans-Fotsing Tetsing, Gilbert Nibaruta, Aboubacar Nibirantiza

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Abstract

We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.

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We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.

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Available abstract

We establish the links between the lightlike geometry and basics invariants of the associated semi-Riemannian geometry on r-lightlike submanifold and semi-Riemannian constructed from a semi-Riemannian ambient. Then we establish some basic inequalities, involving the scalar curvature and shape operator on r-lightlike coisotropic submanifold in semi-Riemannian manifold. Equality cases are also discussed.

Key concepts: Submanifold, Scalar curvature, Mathematics, Curvature, Riemannian manifold, Prescribed scalar curvature problem, Pure mathematics, Sectional curvature

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