Abstract

PICCIONE, Paolo  and  TAUSK, Daniel V.. Connections compatible with tensors: A characterization of left-invariant Levi-Civita connections in Lie groups. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.1, pp.125-133. ISSN 0041-6932.

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 .

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