Geodesic connectedness of semi-Riemannian manifolds
By Miguel Sánchez Caja. 2000
53 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ce22c167bf908908088f1b977189abfd050a43b9
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- On the definition and examples of Finsler metrics (2011, background): “For (iii) and (iv), even though the equivalences between the (strict or not) convexities of B and S are known (see for example [6, 43] and references therein), we will prove the full cyclic implications for the sake of completeness.”