Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773606 | Differential Geometry and its Applications | 2017 | 24 Pages |
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
Stephanie B. Alexander, William A. Karr,