nLab
Euclidean geometry

Context

Geometry

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

Euclidean geometry studies the geometry of Euclidean spaces. These spaces come equipped with a canonical Riemannian metric, and Euclidean geometry can be regarded as the local model for Riemannian geometry, in some sense.

Properties

synthetic geometry
Euclidean geometry
hyperbolic geometry
elliptic geometry
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

Revised on August 13, 2014 09:40:25 by Urs Schreiber (146.96.130.201)