Work

On Gauss-Bonnet Curvatures

Year: 2007

Type: article

Abstract: 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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2007.118

Author: Mohammed Larbi Labbi

Institution: University of Bahrain

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W2133442142

FWCI: 0.4

Cites: 34

Cited by: 16

Related to: 10