Connections compatible with tensors. A characterization of left-invariant Levi--Civita connections in Lie groups

Details Connections compatible with tensors. A characterization of left-invariant Levi--Civita connections in Lie groups Connections compatible with tensors. A characterization of left-invariant Levi--Civita connections in Lie groups

2005-09-28

arxiv.org/abs/math/0509656v1

Mathematics

Differential Geometry

Article for the Proceedings of the EGEO2005, Cordoba, Argentina. LaTeX2e, amsart, 9 pages, no figures

Scientific paper

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi-Civita connection of some semi-Riemannian metric on the group. As a special case, we will consider constant connections in $\R^n$.

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