Rotational hypersurfaces with constant Gauss-Kronecker curvature
Differential Geometry
2022-01-20 v1
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.
Keywords
Cite
@article{arxiv.2201.07415,
title = {Rotational hypersurfaces with constant Gauss-Kronecker curvature},
author = {Yuhang Liu and Yunchu Dai},
journal= {arXiv preprint arXiv:2201.07415},
year = {2022}
}
Comments
To appear in Chinese Annals of Mathematics, series B; 23 pages, 5 figures; comments are welcome