Pseudo-Riemannian Weakly Symmetric Manifolds

Details Pseudo-Riemannian Weakly Symmetric Manifolds Pseudo-Riemannian Weakly Symmetric Manifolds

2011-07-22

arxiv.org/abs/1107.4636v1

Mathematics

Differential Geometry

Nine pages

Scientific paper

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit property, weak symmetries, and the structure of the nilradical of the isometry group. Also, we give a number of examples of weakly symmetric pseudo-Riemannian manifolds, some mirroring the Riemannian case and some indicating the problems in extending Riemannian results to weakly symmetric pseudo-Riemannian spaces.

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