A Ladder of Curvatures in the Geometry of Surfaces

Abstract

Many investigations in the local differential geometry of surfaces focused on Gaussian curvature

and mean curvature. Besides these classical curvature invariants, are there any other geometric

quantities that deserve to be investigated? In the recent decades, there have been important

developments in the area of new curvature invariants for submanifolds, mostly included in Bang-

Yen Chen’s important monograph Pseudo-Riemannian geometry, δ−invariants and applications, World

Scientific, 2011. These developments are inviting us to look at the classical content from a different

perspective, exploring other quantities that might be of interest.

Keywords

• principal curvatures,Gaussian curvature,mean curvature,Casorati curvature,smooth surfaces,conformal Gauss map

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