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

Abstract

B.-Y. Chen’s ^-invariants can be estimated in function of other curvature terms through an algebraicprocess using the AM-GM and AM-QM inequalities. This procedure works on strictly convexsmooth hypersurfaces lying in an Euclidean ambient space, and the estimates relate some ^-invariants to Germain’s mean curvature and Casorati curvature. As a consequence, we obtain anew string of inequalities in the geometry of strictly convex smooth hypersurfaces.