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

Jih-Hsin Cheng; Hung-Lin Chiu; Jenn-Fang Hwang; Paul Yang

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arXiv · 1512.05859

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

Jih-Hsin Cheng·Hung-Lin Chiu·Jenn-Fang Hwang·Paul Yang

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Abstract

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\geq $ $2.$ 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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BibTeX RIS

Jih-Hsin Cheng, Hung-Lin Chiu, Jenn-Fang Hwang, Paul Yang. 2015-12-18. Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group. https://arxiv.org/abs/1512.05859

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