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On Gauss-Bonnet Curvatures
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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On Gauss-Bonnet Curvatures
Інший ID:
2000 Mathematics Subject Classification: 53C20; 53C25
Посилання:
On Gauss-Bonnet Curvatures / M.L. Labbi // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 38 назв. — англ.
Підтримка:
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.
Дата:
2007
Переглядів:
506
Завантажень:
165
Анотація:
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.
