Scalar curvature of definable CAT-spaces

被引：9

作者：

Bernig, A ^{[1
]}

机构：

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

来源：

ADVANCES IN GEOMETRY | 2003年 / 3卷 / 01期

关键词：

O-MINIMAL STRUCTURES; SETS;

D O I：

10.1515/advg.2003.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the scalar curvature measure for sets belonging to o-minimal structures (e.g. semialgebraic or subanalytic sets) from the viewpoint of metric differential geometry. Theorem: Let S be a compact connected definable pseudo-manifold with curvature bounded from above, then the singular part of the scalar curvature measure is non-positive. The topological restrictions cannot be removed, as is shown in examples.

引用

页码：23 / 43

页数：21

共 11 条

[1]

Bernig A, 2002, ADV GEOM, V2, P29

[2] Integral geometry of tame sets [J].