On the uniqueness of complete biconservative surfaces in ℝ³

2017/11/20 by Nistor, Simona, Oniciuc, Cezar
#57N05 #Differential Geometry (math.DG) #FOS: Mathematics #General Topology (math.GN) #Primary 53A05 #Secondary 53C42

paper · doi:10.48550/arxiv.1711.07253

Abstract

We study the uniqueness of complete biconservative surfaces in the Euclidean space ℝ³, and prove that the only complete biconservative regular surfaces in ℝ³ are either CMC or certain surfaces of revolution. In particular, any compact biconservative regular surface in ℝ³ is a round sphere.

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