A General Optimal Inequality for Arbitrary Riemannian Submanifolds
نویسندگان
چکیده
One of the most fundamental problems in submanifold theory is to establish simple relationships between intrinsic and extrinsic invariants of the submanifolds (cf. [6]). A general optimal inequality for submanifolds in Riemannian manifolds of constant sectional curvature was obtained in an earlier article [5]. In this article we extend this inequality to a general optimal inequality for arbitrary Riemannian submanifolds in an arbitrary Riemannian manifold. This new inequality involves only the δ-invariants, the squared mean curvature of the submanifolds and the maximum sectional curvature of the ambient manifold. Several applications of this new general inequality are also presented.
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