arXiv:math/0005039 Abstract

arXiv:math/0005039 [math.DG]Abstract References Reviews Resources

Geodesic connectedness of semi-Riemannian manifolds

Published 2000-05-04, updated 2000-09-12Version 2

The question whether a Riemannian manifold is geodesically connected can be studied from geometrical as well as variational methods, and accurate results can be obtained by using the associated distance and related properties of the positive-definiteness. It is natural to state this problem in manifolds with (possibly non-smooth) boundary, and some conditions on this boundary has been studied. For Lorentzian manifolds, the results cannot be so general, and very different techniques has been introduced which are satisfactory for some classes of Lorentzian manifolds: spaceforms, disprisoning and pseudoconvex manifolds, stationary, globally hyperbolic or multiwarped spacetimes... Some of them are appliable to semi-Riemannian manifolds with higher index or even to manifolds with just an affine connection. Our purpose is to review these semi-Riemannian techniques, discussing the results and possible extensions.

Comments: 14 pages, Latex; revised version with minor changes; a shortened version of 12 pages will appear at Nonlinear Anal. (proceedings WCNA'00)

Categories: math.DG

Subjects: 53C50, 53C22, 58E10

Keywords: semi-riemannian manifolds, geodesic connectedness, lorentzian manifolds, higher index, variational methods

Related articles: Most relevant | Search more

arXiv:math/0004075 [math.DG] (Published 2000-04-12)

Convexity of domains of Riemannian manifolds

Rossella Bartolo, Anna Germinario, Miguel Sanchez

arXiv:math/9909075 [math.DG] (Published 1999-09-14)

Geodesic connectedness of multiwarped spacetimes

Jose L. Flores, Miguel Sanchez

arXiv:1106.0211 [math.DG] (Published 2011-06-01)

A note on geodesic connectedness of Gödel type spacetimes