具平坦欧氏边界的局部凸浸入超曲面（英文）  

Locally convex immersed surface with flat Euclidean boundary

作　　者：王宝富[1] WANG Bao-Fu(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院

出　　处：《四川大学学报（自然科学版）》2020年第1期7-10,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11571242)

摘　　要：在仿射微分几何中,局部强(一致)凸的浸入超曲面的几何与拓扑性质非常复杂.本文构造出一类新的局部强凸的浸入超曲面,其欧氏边界是平坦的(即边界落在一个超平面内),但曲面本身却不是整体凸的.这与目前已有的结论完全不同.In differential geometry,the geometric and topological behaviors of locally strongly(uniformly)convex immersed surfaces(hypersurfaces)are very complicated,so are their Euclidean boundaries.In this paper,we construct new locally strongly convex(but not globally convex)immersed surfaces(hypersurfaces)with flat Euclidean boundary in R n+1(n=2,3),which are different from an existing conclusion.

关 键 词：浸入超曲面 欧氏边界点 局部强凸 

分 类 号：O186.12[理学—数学]