Bernig, A (2003). Variation of curvatures of subanalytic spaces and Schläfli-type formulas. Annals of Global Analysis and Geometry, 24(1):67-93.
We prove a strong variational formula for Lipschitz–Killing curvaturesof subanalytic sets. As corollaries, we reprove the Chern–Gauss–Bonnettheorem and higher Schläfli formulas. The proof of the variationalformula uses normal cycles of subanalytic sets and a new method allowinga reduction from the difficult singular geometry to computations withdifferential forms.
We prove a strong variational formula for Lipschitz–Killing curvaturesof subanalytic sets. As corollaries, we reprove the Chern–Gauss–Bonnettheorem and higher Schläfli formulas. The proof of the variationalformula uses normal cycles of subanalytic sets and a new method allowinga reduction from the difficult singular geometry to computations withdifferential forms.
| 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 > Analysis
Social Sciences & Humanities > Political Science and International Relations Physical Sciences > Geometry and Topology |
| Uncontrolled Keywords: | normal cycle - subanalytic set - Schläfli - Lipschitz–Killing curvature - scalar curvature - Einstein equation |
| Language: | English |
| Date: | 2003 |
| Deposited On: | 29 Nov 2010 16:26 |
| Last Modified: | 25 Feb 2020 12:44 |
| Publisher: | Springer |
| ISSN: | 0232-704X |
| OA Status: | Closed |
| Publisher DOI: | https://doi.org/10.1023/A:1024269221528 |
| Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1990086 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1037.32012 |
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Bernig, A