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Scalar curvature of definable CAT-spaces


Bernig, A (2003). Scalar curvature of definable CAT-spaces. Advances in Geometry, 3(1):23-43.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:De Gruyter
ISSN:1615-715X
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

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