Difference between revisions of "Main Page"

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(Creating a table of contents)
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=Contents=
 
=Contents=
  
*[Lie group]
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==Basics==
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*[[Topological manifold]]
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*[[Differential manifold]]
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*[[Riemannian manifold]]
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*[[Connection]]
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*[[Lie group]]
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===Properties of connections===
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*[[Linear connection]]
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*[[Torsion of a linear connection]]
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*[[Torsion-free linear connection]]
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===Basic kinds of metrics===
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*[[Riemannian metric]]
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*[[Homogeneous metric]]
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*[[Locally homogeneous metric]]
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==Classification of differential manifolds according to the structure group==
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*[[Pseudo-Riemannian manifold]]
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*[[Almost Hermitian manifold]]
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*[[Almost complex manifold]]
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*[[Almost symplectic manifold]]
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*[[Lorentzian manifold]]
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*[[Oriented manifold]]
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==Curvatures==
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*[[Riemann curvature tensor]]
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*[[Ricci curvature tensor]]
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*[[Scalar curvature]]
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*[[Sectional curvature]]
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*[[Total scalar curvature]]
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*[[Total absolute scalar curvature]]
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*[[Average scalar curvature]]
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*[[Mean curvature]]
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*[[Average mean curvature]]
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==Classification of metrics according to curvatures==
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*[[Flat metric]]
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*[[Ricci-flat metric]]
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*[[Einstein metric]]
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*[[Constant-curvature metric]]
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*[[Constant-scalar curvature metric]]
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*[[Zero-scalar curvature metric]]
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==Special scalar functions on Riemannian manifolds==
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*[[Injectivity radius of a manifold]]
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*[[Isoperimetric constant]]
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*[[Pinching constant]]
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==Various theorems==
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===Results on Ricci curvature===
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*[[Bonnet-Myers theorem]]
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*[[Schoen-Yau theorem]]
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*[[Zhu's theorem]]
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*[[Splitting theorem]]
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===Results on sectional curvature===
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*[[Cheeger-Gromoll conjecture]]
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*[[Cohn-Vossen theorem]]
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*[[Gromoll-Meyer theorem]]
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*[[Cartan-Hadamard theorem]]
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*[[Bieberbach theorem]]
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*[[Finiteness theorem]]
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*[[Schur's theorem]]
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*[[Synge's theorem]]
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===Results relating curvature to topology===
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*[[Bieberbach theorem]]
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*[[Bonnet-Myers theorem]]
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*[[Cartan-Hadamard theorem]]
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*[[Gauss-Bonnet theorem]]
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*[[Synge's theorem]]
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*[[Preissmann's theorem]]
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 +
 
 +
 
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*[[Splitting theorem]]
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==Special topics==
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*[[Minimal manifold]]
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*[[Characteristic class]]
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*[[Chern form]]
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*[[Chern-Weil theorem]]

Revision as of 20:13, 7 July 2007

This is Diffgeom (the Differential Geometry wiki).

Much of it is patterned on the Group Properties wiki.

It is currently in a very preliminary stage and may contain a number of factual errors. It is meant only for private use.

It may never become sturdy enough for public use!

Contents

Basics

Properties of connections

Basic kinds of metrics

Classification of differential manifolds according to the structure group

Curvatures

Classification of metrics according to curvatures

Special scalar functions on Riemannian manifolds

Various theorems

Results on Ricci curvature

Results on sectional curvature

Results relating curvature to topology


Special topics