Connections Compatible with Tensors. a Characterization of Left-invariant Levi–civita Connections in Lie Groups
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چکیده
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 n.
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تاریخ انتشار 2005