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

Research paper by Paolo Piccione, Daniel V. Tausk

Indexed on: 28 Sep '05Published on: 28 Sep '05Published in: Mathematics - Differential Geometry



Abstract

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 $\R^n$.