nLab
Riemannian geometry

Context

Riemannian geometry

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

Riemannian geometry studies smooth manifolds that are equipped with a Riemannian metric: Riemannian manifolds.

local model spaceglobal geometrydifferential cohomologyfirst order formulation of gravity
generalKlein geometryCartan geometryCartan connection
examplesEuclidean geometryRiemannian geometryaffine connectionEuclidean gravity
Lorentzian geometrypseudo-Riemannian geometryspin connectionEinstein gravity
Lorentzian supergeometysupergeometrysuperconnectionsupergravity
generalKlein 2-geometryCartan 2-geometry
higher Klein geometryhigher Cartan geometryhigher Cartan connection
examplesextended super Minkowski spacetimeextended supergeometryhigher supergravity: type II, heterotic, 11d

In index theory:

References

  • Isaac Chavel, Riemannian geometry – A modern introduction Cambridge University Press (1993)
  • Marcel Berger, A panoramic view of Riemannian geometry
Revised on March 11, 2014 08:42:23 by Urs Schreiber (89.204.139.47)