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arXiv · 2201.07415

Rotational hypersurfaces with constant Gauss-Kronecker curvature

Yuhang Liu·Yunchu Dai
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Abstract

We study rotational hypersurfaces with constant Gauss-Kronecker curvature. We solve the ODE for the generating curves of such hypersurfaces and analyze several geometric properties of such hypersurfaces. In particular, we discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere. Finally we investigate other types of rotational hypersurfaces with similar curvature constraints, including those with prescribed Gauss-Kronecker curvature.

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Yuhang Liu, Yunchu Dai. 2022-01-19. Rotational hypersurfaces with constant Gauss-Kronecker curvature. https://arxiv.org/abs/2201.07415

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