On the Gauss curvature of compact surfaces in homogeneous 3-manifolds

2009/03/10 by Torralbo, Francisco, Urbano, Francisco · 1 citation
#53C30 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.1735

Abstract

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

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• Uniqueness of the Bonnet problem in Thurston geometries

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