Labbi, Mohammed-Larbi

On Gauss-Bonnet curvatures

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 118, 11 p., electronic only (2007)


Summary: 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.

Mathematics Subject Classification

53C20, 53C25


Gauss-Bonnet curvatures, Gauss-Bonnet gravity, Lovelock gravity, generalized Einstein metrics, generalized minimal submanifolds, generalized yamabe problem