moduli space of Riemannian metrics
Hodge inner product, Hodge star operator
gradient, gradient flow
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synthetic differential geometry
synthetic differential supergeometry
. infinitesimal cohesion
de Rham space
formally smooth morphism, formally unramified morphism, formally étale morphism
Models for Smooth Infinitesimal Analysis
smooth algebra (C ∞C^\infty-ring)
smooth manifold, formal smooth manifold, derived smooth manifold
smooth space, diffeological space, Frölicher space
smooth natural numbers
synthetic differential ∞-groupoid
vector field, tangent Lie algebroid;
differentiation, chain rule
differential equation, variational calculus
connection on a bundle, connection on an ∞-bundle
Whitney extension theorem
Steenrod-Wockel approximation theorem
de Rham theorem
Lie theory, ∞-Lie theory
Chern-Weil theory, ∞-Chern-Weil theory
Klein geometry, Klein 2-geometry, higher Klein geometry
Euclidean geometry, Cartan geometry, higher Cartan geometry
For (X,g)(X,g) a Riemannian manifold or pseudo-Riemannian manifold its isometry group
is that subgroup of the group of all diffeomorphisms ϕ:X→X\phi : X \to X that are isometries: which preserve the metric gg in that
The Lie algebra of Iso(X,g)Iso(X,g) is spanned by the Killing vectors of (X,g)(X,g).
The isometry group of Minkowski spacetime is the Poincaré group.
The isometry group of anti de Sitter spacetime is the anti de Sitter group.
The isometry group of de Sitter spacetime is the de Sitter group.