differential geometry
synthetic differential geometry
smooth topos
infinitesimal space
Kock-Lawvere axiom
integration axiom
microlinear space
synthetic differential supergeometry
. infinitesimal cohesion
de Rham space
formally smooth morphism, formally unramified morphism, formally étale morphism
jet bundle
Models for Smooth Infinitesimal Analysis
Fermat theory
smooth algebra (C ∞-ring)
smooth locus
smooth manifold, formal smooth manifold, derived smooth manifold
smooth space, diffeological space, Frölicher space
smooth natural numbers
Cahiers topos
smooth ∞-groupoid
synthetic differential ∞-groupoid
tangent bundle,
vector field, tangent Lie algebroid;
differentiation, chain rule
differential forms
differential equation, variational calculus
connection on a bundle, connection on an ∞-bundle
Riemannian manifold
Hadamard lemma
Borel's theorem
Boman's theorem
Steenrod-Wockel approximation theorem
Poincare lemma
Stokes theorem
de Rham theorem
Chern-Weil theory
Lie theory, ∞-Lie theory
Chern-Weil theory, ∞-Chern-Weil theory
gauge theory
∞-Chern-Simons theory
Klein geometry, Klein 2-geometry, higher Klein geometry
Euclidean geometry, Cartan geometry, higher Cartan geometry
Riemannian geometry
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An almost Hermitian structure on an almost complex manifold is a further reduction of the structure group of the tangent bundle along the inclusion of the unitary group U(n)↪GL(n,ℂ).