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On Gauss-Bonnet Curvatures

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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Main Author: Labbi, M.L.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147209
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spelling irk-123456789-1472092019-02-14T01:24:10Z On Gauss-Bonnet Curvatures Labbi, M.L. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147209 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Labbi, M.L.
spellingShingle Labbi, M.L.
On Gauss-Bonnet Curvatures
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Labbi, M.L.
author_sort Labbi, M.L.
title On Gauss-Bonnet Curvatures
title_short On Gauss-Bonnet Curvatures
title_full On Gauss-Bonnet Curvatures
title_fullStr On Gauss-Bonnet Curvatures
title_full_unstemmed On Gauss-Bonnet Curvatures
title_sort on gauss-bonnet curvatures
publisher Інститут математики НАН України
publishDate 2007
url http://dspace.nbuv.gov.ua/handle/123456789/147209
citation_txt On Gauss-Bonnet Curvatures / M.L. Labbi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 38 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT labbiml ongaussbonnetcurvatures
first_indexed 2023-05-20T17:26:50Z
last_indexed 2023-05-20T17:26:50Z
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