Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools

Details Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools

2006-10-04

arxiv.org/abs/math/0610144v2

In: "Recent developments in pseudo-Riemannian Geometry" (D.V. Alekseevsky & H. Baum Eds), Special Volume in the ESI-Series on

Mathematics

Differential Geometry

Scientific paper

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry. The progress in the last two decades has become impressive, being especially relevant the systematic introduction of (infinite-dimensional) variational methods. Our purpose is to give an overview, from refinements of classical results to updated variational settings. First, several properties (and especially completeness) of geodesics in some ambient spaces are studied. This includes heuristic constructions of compact incomplete examples, geodesics in warped, GRW or stationary spacetimes, properties in surfaces and spaceforms, or problems on stability of completeness. Then, we study the variational framework, and focus on two fundamental problems of this approach, which regards geodesic connectedness. The first one deals with a variational principle for stationary manifolds, and its recent implementation inside Causality Theory. The second one concerns orthogonal splitting manifolds, and a reasonably self-contained development is provided, collecting some steps spread in the literature.

Affiliated with

Also associated with

No associations

Rating

Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-155970