nLab
projectively flat connection

Idea

A connection that is flat up to a central term.

In Cartan geometry, a torsion-free affine connection \nabla on a manifold is said to be projectively flat if the corresponding normal projective Cartan connection induced by the projective class of \nabla is flat. For example, the Levi-Civita connection of a hyperbolic manifolds are projectively flat in this sense, because the corresponding normal standard tractor connection is flat.

Last revised on July 19, 2018 at 21:53:51. See the history of this page for a list of all contributions to it.