nLab projective structure

This is a disambiguation page.

Word projective structure may mean a projective model structure where model structure is in the sense of Quillen model structure and it may refer to such a “projective” model structures in a variety of contexts, most classically on a category of 1-sided modules over a ring and also in the context of model structure on functors.

It may also mean one of the Cartan geometries (locally homogeneous geometric structures), which is locally modeled on a projective space. This subject or its underlying object is sometimes called projective differential geometry, projective Cartan geometry, locally projective geometry, locally projective manifold, or a manifold with a (locally) projective structure.

It may also refer to one of the - realizations of/formalisms for - the projective structures, for example a projective atlas on a manifold or a projective Cartan connection. See also projectively flat connection.

• William Goldman, What is a… projective structure, Notices Amer. Math. Soc., November 2008, pdf