A Ladder of Curvatures in the Geometry of Surfaces

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International Electronic Journal of Geometry
Volume:11 Issue:2
A Ladder of Curvatures in the Geometry of Surfaces

A Ladder of Curvatures in the Geometry of Surfaces

Authors : Nicholas D BRUBAKER, Jasmine CAMERO, Oscar Rocha ROCHA, Bogdan D SUCEAVA

Pages : 28-33

View : 46 | Download : 9

Publication Date : 2018-11-30

Article Type : Research Paper

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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