Bernig, A (2003). Scalar curvature of definable CAT-spaces. Advances in Geometry, 3(1):23-43.
We study the scalar curvature measure for sets belonging to o-minimal structures (e.g. semialgebraic or subanalytic sets) from the viewpoint of metric dierential 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 topo- logical restrictions cannot be removed, as is shown in examples.
We study the scalar curvature measure for sets belonging to o-minimal structures (e.g. semialgebraic or subanalytic sets) from the viewpoint of metric dierential 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 topo- logical restrictions cannot be removed, as is shown in examples.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Geometry and Topology |
| Language: | English |
| Date: | 2003 |
| Deposited On: | 29 Nov 2010 16:26 |
| Last Modified: | 23 Jan 2022 14:37 |
| Publisher: | De Gruyter |
| ISSN: | 1615-715X |
| OA Status: | Green |
| Free access at: | Related URL. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1515/advg.2003.003 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1956586 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1028.53031 http://www.math.ethz.ch/EMIS/journals/AG/3-1/3_23.pdf |
Bernig, A