A Simons type formula for surfaces with parallel mean curvature

2011/02/01 by Dorel Fetcu, Fetcu, Dorel, Harold Rosenberg +1
Mathematics · #53A10 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A10 #msc:53C42

paper · pdf · doi:10.48550/arxiv.1102.0219

This paper has been withdrawn by the authors because equation 3.13 (the Simons type equation) is a particular case of formula 2.8 in [S.-Y. Cheng and S.-T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225(1977), 195--204

arxiv created 2011/02/02 · arxiv updated 2011/02/03

Abstract

We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in Mⁿ(c)×ℝ, where Mⁿ(c) is an n-dimensional space form. Then, we use this equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.

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