Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature  

作　　者：Yuhang LIU Yunchu DAI 

机构地区：[1]Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China [2]Department of Mathematics,Stanford University,California 94305,USA

出　　处：《Chinese Annals of Mathematics,Series B》2022年第3期343-358,共16页数学年刊（B辑英文版）

基　　金：Peking University for providing financial support for the first author

摘　　要：The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they 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.

关 键 词：Differential geometry Gauss-Kronecker curvature Ordinary differential equation 

分 类 号：O186.1[理学—数学]