- International Electronic Journal of Geometry
- Volume:12 Issue:1
- Estimates of B.-Y. Chen’s δˆ-Invariant in Terms of Casorati Curvature and Mean Curvature for Strictl...
Estimates of B.-Y. Chen’s δˆ-Invariant in Terms of Casorati Curvature and Mean Curvature for Strictly Convex Euclidean Hypersurfaces
Authors : Bogdan D SUCEAVA, Mihaela B VAJİAC
Pages : 26-31
View : 49 | Download : 8
Publication Date : 2019-03-27
Article Type : Research Paper
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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