Article ID Journal Published Year Pages File Type
5773606 Differential Geometry and its Applications 2017 24 Pages PDF
Abstract
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds. Specifically, we study geodesic connectedness. We give geometric-topological proofs of geodesic connectedness for classes of space-times to which known methods do not apply. For instance: A null-disprisoning space-time is geodesically connected if it supports a proper, nonnegative strictly convex function whose critical set is a point. Timelike strictly convex hypersurfaces of Minkowski space are geodesically connected. We also give a criterion for the existence of a convex function on a semi-Riemannian manifold. We compare our work with previously known results.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, ,