Diffgeom:Content scope

This article is about the diffgeom wiki itself

The Differential Geometry wiki is concerned mainly with the theory of differential manifolds as well as the theory of important additional sturctures on differential manifolds, such as Riemannian metrics, pseudo-Riemannian metrics, symplectic structures, contact structures, Hermitian structures, and complex structures.

What diffgeom wiki has or aims to have

Thrust areas

• Information on differential manifolds (the category of differential manifolds with $k$ times or infinitely differentiable maps)
• Information on Riemannian metrics and structures associated with Riemannian metrics, particularly notions of curvature, geodesics
• An understanding of the relation between differential/Riemannian structure and the topology of the underlying manifold

Other areas

• General notions of additional structure on differential manifolds
• Flows on differential manifolds, such as the Ricci flow
• The use of homology and cohomology in the study of manifolds
• Interplay with complex structure

What diffgeom does not want to have right now

The following areas are closely related to differential geometry but we do not aim to make them a part of diffgeom, at least as of now:

• Theories and results in point-set topology and algebraic topology: The right place for these is the Topology wiki
• Theories and results in complex geometry: The right place for these is the Complex Geometry wiki