论文标题
具有恒定高斯 - kronecker曲率的旋转高度曲面
Rotational hypersurfaces with constant Gauss-Kronecker curvature
论文作者
论文摘要
我们研究具有恒定高斯 - kronecker曲率的旋转曲面。我们求解了此类超曲面的生成曲线的ode，并分析了此类超曲面的几种几何特性。特别是，我们发现了一类具有恒定和负高斯 - 克罗内克曲率和有限体积的非紧凑型旋转高度曲面，可以看作是伪速率的较高维度的概括。最后，我们研究了具有相似曲率约束的其他类型的旋转超曲面，包括那些具有开处方的高斯 - 凯伦克曲率的旋转曲面。
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.
