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

Yıl 2019, Cilt: 12 Sayı: 1, 26 - 31, 27.03.2019

Bogdan D. Suceava Mihaela B. Vajiac

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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