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This is Welcome to Diffgeom (the Differential Geometry wiki).!
Much Diffgeom is currently in a pre-formed state, and much of it is patterned the information entered here may be incorrect, misleading or unreliable. Please do ''not'' rely on the [ Group Properties wiki]information or content here.
It is currently in a very preliminary stage and may contain a number of factual errors. It is meant only for private use.==Using Diffgeom==
It may never become sturdy enough for public * '''How do I use!Diffgeom?'''
=Contents= ==Basics== *[[Topological manifold]]*[[Differential manifold]]*[[Riemannian manifold]]*[[Connection]]*[[Lie group]] ===Properties of connections=== *[[Linear connection]]*[[Torsion of a linear connection]]*[[Torsion-free linear connection]] ===Basic kinds of metrics=== *[[Riemannian metric]]*[[Homogeneous metric]]*[[Locally homogeneous metric]] ==Classification of differential manifolds according We are ourselves trying to the structure group== *[[Pseudo-Riemannian manifold]]*[[Almost Hermitian manifold]]*[[Almost complex manifold]]*[[Almost symplectic manifold]]*[[Lorentzian manifold]]*[[Oriented manifold]] ==Curvatures== *[[Riemann curvature tensor]]*[[Ricci curvature tensor]]*[[Scalar curvature]]*[[Sectional curvature]]*[[Total scalar curvature]]*[[Total absolute scalar curvature]]*[[Average scalar curvature]]*[[Mean curvature]]*[[Average mean curvature]] ==Classification of metrics according figure out answers to curvatures== *[[Flat metric]]*[[Ricci-flat metric]]*[[Einstein metric]]*[[Constant-curvature metric]]*[[Constant-scalar curvature metric]]*[[Zero-scalar curvature metric]] ==Special scalar functions that! Diffgeom has been patterned on Riemannian manifolds== *[[Injectivity radius the lines of a manifold]]*[[Isoperimetric constant]]*[[Pinching constant]] ==Various theorems== ===Results on Ricci curvature=== *[[Bonnet-Myers theorem]]*[[Schoen-Yau theorem]]*[[Zhu's theorem]]*[[Splitting theorem]] ===Results on sectional curvature=== *[[Cheeger-Gromoll conjecture]]*[[Cohn-Vossen theorem]]*[[Gromoll-Meyer theorem]]*[[Cartan-Hadamard theorem]]*[[Bieberbach theorem]]*[[Finiteness theorem]]*[[Schur's theorem]]*[[Synge's theorem]] ===Results relating curvature Groupprops, the group theory wiki. We intend to topology=== *[[Bieberbach theorem]]*[[Bonnet-Myers theorem]]*[[Cartan-Hadamard theorem]]*[[Gauss-Bonnet theorem]]*[[Synge's theorem]]*[[Preissmann's theorem]]   *[[Splitting theorem]] ==Special topics== *[[Minimal manifold]]*[[Characteristic class]]*put up the following pages soon: [[Chern formDiffgeom:Guided tour]]*and [[Chern-Weil theoremDiffgeom:Exploration]].
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