Reductive locally homogeneous pseudo-Riemannian manifolds and Ambrose-Singer connections

Ignacio Luján

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arXiv · 1405.0826

Reductive locally homogeneous pseudo-Riemannian manifolds and Ambrose-Singer connections

Ignacio Luján

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Abstract

Ambrose and Singer characterized connected, simply-connected and complete homogeneous Riemannian manifolds as Riemannian manifolds admitting a metric connection such that its curvature and torsion are parallel. The aim of this paper is to extend Ambrose-Singer Theorem to the general framework of locally homogeneous pseudo-Riemannian manifolds. In addition we study under which conditions a locally homogeneous pseudo-Riemannian manifold can be recovered from the curvature and their covariant derivatives at some point up to finite order. The same problem is tackled in the presence of a geometric structure.

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Ignacio Luján. 2014-05-05. Reductive locally homogeneous pseudo-Riemannian manifolds and Ambrose-Singer connections. https://arxiv.org/abs/1405.0826

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