A ladder of curvatures for hypersurfaces in the Euclidean ambient space

Abstract

We introduce a string of new curvature invariants of a hypersurface in the real (n + 1)-dimensional space and we establish a ladder of inequalities involving these curvature invariants. There is an analogy between this series of inequalities and the classical ladder of power means for positive real numbers. To describe the natural geometric interpretation of our proposed construction we refer to B. Riemann's original idea of sectional curvature.

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