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

Paolo Piccione; Daniel V. Tausk

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

Paolo Piccione·Daniel V. Tausk

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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 $\R^n$.

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Paolo Piccione, Daniel V. Tausk. 2005-09-28. Connections compatible with tensors. A characterization of left-invariant Levi--Civita connections in Lie groups. https://arxiv.org/abs/math/0509656

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