Gaussian curvature in codimension > 1

2013/12/09 by Alvarez-Gavela, Daniel
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2554

Abstract

The Gaussian curvature K is a fundamental geometric quantity discovered by Gauss in the case of surfaces embedded in ℝ³. One can naturally extend the definition of the Gaussian curvature to arbitrary submanifolds of ℝ^k so that the extrinsic interpretation of K, the Theorema Egregium and the Gauss-Bonnet Theorem still hold. We give a concise exposition of these classical facts.

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