Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

2015/12/18 by Cheng, Jih-Hsin, Chiu, Hung-Lin, Hwang, Jenn-Fang +1 · 1 citation
#32V20 #35J70 #35L80 #49Q10 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.05859

Abstract

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group H_n with n ≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

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• The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups H_n

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