2022/01/19 by Yuhang Liu, Liu, Yuhang, Yunchu Dai +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Mathematics and Applications #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2201.07415
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.