A DIFFERENTIAL GEOMETRIC CHARACTERIZATION OF HOMOGENEOUS SELF-DUAL CONES
A DIFFERENTIAL GEOMETRIC CHARACTERIZATION OF HOMOGENEOUS SELF-DUAL CONES
复制标题
均质自对偶锥体的微分几何表征
DOI：
10.21099/tkbjm/1496159452
复制
发表时间：
1982
影响因子：
0.7
通讯作者：
H. Shima
中科院分区：
文献类型：
--
作者：
H. Shima
定义一个张量场？，我们用同样的字母f来表示这个张量场。Vn中的开放凸集Q称为顶点为o的锥，如果0 +/l(x-o)qQ对于所有a；和^ > 0。一个顶点为0的开凸锥Q是一个自对偶锥，如果Vn允许一个内积满足(i) (x - o,y - 0>> o对于所有x，y - Q; （ii）如果# F”是一个向量，使得o - o，y - ^0对于所有y - Q，则a；ei2 （wh^ r0）等于thp。冲洗；冲洗；0 in Vn
defines a tensor fieldon £?,we denote this tensor fieldby the same letter F. An open convex set Q in Vn is called a cone with vertex o if o+/l(x―o)qQ for all a;eX?and ^>0. An open convex cone Q with vertex o is said to be a selfdual cone if Vn admits an inner product such that (i) (x ―o,y ―0>>O for all x,y£Q; (ii) if # F" is a vector such that O ―o,y― ^0 for all y£Q then a;ei2, wh^rp O is thp.rinsnrp of .0 in Vn