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2011•TURKISH JOURNAL OF MATHEMATICSOpen access

B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature

Cıhan Özgür

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Abstract

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

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What this paper is about

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

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Available abstract

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

Key concepts: Scalar curvature, Mathematics, Sectional curvature, Ricci curvature, Space form, Riemannian manifold, Curvature, Pure mathematics

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