Some Curvature Problems in Semi-Riemannian Geometry

Abstract

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.

25 pages, LaTeX, 4 figures

References in corpus (5)

• Present status of the Penrose inequality
• A Level Set Analysis of the Witten Spinor with Applications to Curvature Estimates
• Pseudo-Riemannian metrics with prescribed scalar curvature
• A remark on the rigidity case of the positive energy theorem
• Nonexistence of spacelike foliations and the dominant energy condition in Lorentzian geometry

Cited by in corpus (1)

• Non-perturbative analysis of the constraints and the positivity of the energy of the complete Horava theory