Estimates of B.-Y. Chen’s δˆ-Invariant in Terms of Casorati Curvature and Mean Curvature for Strictly Convex Euclidean Hypersurfaces

Year 2019, Volume: 12 Issue: 1, 26 - 31, 27.03.2019

Bogdan D. Suceava , Mihaela B. Vajiac

Abstract

B.-Y. Chen’s δˆ-invariants can be estimated in function of other curvature terms through an algebraic

process using the AM-GM and AM-QM inequalities. This procedure works on strictly convex

smooth hypersurfaces lying in an Euclidean ambient space, and the estimates relate some  δˆ-

invariants to Germain’s mean curvature and Casorati curvature. As a consequence, we obtain a

new string of inequalities in the geometry of strictly convex smooth hypersurfaces.

Keywords

principal curvatures, Casorati curvature, mean curvature, smooth hypersurfaces, AM QM inequality

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