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2008-05-18T20:13:34Z

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Vipul at 06:21, 23 May 2007

2007-05-23T06:21:10Z

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{{diffgeom}}

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

==What diffgeom wiki has or aims to have==

===Thrust areas===

* Information on [[differential manifold]]s (the category of differential manifolds with <math>k</math> times or infinitely differentiable maps)
* Information on [[Riemannian metric]]s and structures associated with Riemannian metrics, particularly notions of [[curvature]], [[geodesic]]s
* 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 [http://topospaces.wiki-site.com Topology wiki]
* Theories and results in complex geometry: The right place for these is the [http://complexgeom.wiki-site.com Complex Geometry wiki]

Diffgeom:Content scope - Revision history

Vipul: 1 revision

Vipul at 06:21, 23 May 2007