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: Labbi, M.L.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
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
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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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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
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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