On Gauss-Bonnet Curvatures
The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k =1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where t...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147209 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Gauss-Bonnet Curvatures / M.L. Labbi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 38 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862704103425048576 |
|---|---|
| author | Labbi, M.L. |
| author_facet | Labbi, M.L. |
| citation_txt | On Gauss-Bonnet Curvatures / M.L. Labbi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 38 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k =1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.
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| first_indexed | 2025-12-07T16:50:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147209 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:50:47Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Labbi, M.L. 2019-02-13T19:06:09Z 2019-02-13T19:06:09Z 2007 On Gauss-Bonnet Curvatures / M.L. Labbi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 38 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53C20; 53C25 https://nasplib.isofts.kiev.ua/handle/123456789/147209 The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k =1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds. This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. The author would like to thank the referees for useful comments and especially for indicating me the related work of Patterson. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Gauss-Bonnet Curvatures Article published earlier |
| spellingShingle | On Gauss-Bonnet Curvatures Labbi, M.L. |
| title | On Gauss-Bonnet Curvatures |
| title_full | On Gauss-Bonnet Curvatures |
| title_fullStr | On Gauss-Bonnet Curvatures |
| title_full_unstemmed | On Gauss-Bonnet Curvatures |
| title_short | On Gauss-Bonnet Curvatures |
| title_sort | on gauss-bonnet curvatures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147209 |
| work_keys_str_mv | AT labbiml ongaussbonnetcurvatures |