List of differential geometry topics - Definition and Overview

This is a list of differential geometry topics, by Wikipedia page. See also glossary of differential and metric geometry, list of Lie group topics.

Differential geometry of curves

• Frenet-Serret formulas
• Curves in differential geometry
• Line element

Differential geometry of surfaces

• Ruled surface
• Conical surface
• Mean curvature
• Theorema egregium
• Gauss-Bonnet theorem

Calculus on manifolds

See also multivariate calculus, list of multivariable calculus topics

• Manifold
• Tangent vector
• Tangent space
• Tangent bundle
• Cotangent space
• Cotangent bundle
• Vector bundle
• Vector field
• Tensor field
• Differential form
• Exterior derivative
• Frobenius theorem
• Contact (mathematics)

Differential topology

• Diffeomorphism
  • Large diffeomorphism
• Orientability
• Whitney embedding theorem
• Critical value
• Saddle point
• Morse theory
• Lie derivative
• Hairy ball theorem
• Poincaré-Hopf theorem
• Stokes' theorem
• De Rham cohomology
• Smale's paradox

Fiber bundles

• Fiber bundle
• Principal bundle
  • Frame bundle
  • Hopf bundle
• Associated bundle
• Vector bundle
  • Tangent bundle
  • Cotangent bundle
  • Line bundle
• Jet bundle

Riemannian geometry

• Metric tensor
• Riemannian manifold
• Non-Euclidean geometry
  • Angle excess
  • Sphere-world
• Hodge star operator
• Killing vector field
• Geodesic
  • Prime geodesic
• Geodesic flow
• Exponential map
• Injectivity radius
• Jacobi field
• Uniformization theorem
• Myers theorem
• Symmetric space
• Hypersurface
• Nash embedding theorem
• Gromov's compactness theorem
• Hsiang-Lawson's conjecture
• Riemannian submanifold

Variant structures

• Intrinsic metric
• Pseudo-Riemannian manifold
• Sub-Riemannian manifold
• General relativity
• Holonomy, local holonomy
• G-structure
• Complex manifold,
• Almost complex manifold
• Kähler manifold
  • Calabi-Yau spaces
• Hyperkähler manifold
• Symplectic topology
• Contact geometry
• G2 manifold
• Foliation
• Integrability conditions for differential systems
• Finsler geometry
• Information geometry

Curvature

Main article curvature of Riemannian manifolds

• Theorema Egregium
• Gauss-Bonnet theorem
• Gauss map
• Second fundamental form
• Curvature vector
• Curvature form
• Curvature tensor
• Geodesic curvature
• Scalar curvature
• Sectional curvature
• Ricci curvature, Ricci flat
• Weyl curvature
• Ricci flow
• Minimal surface
• Connection
  • Connection form
    • Chern-Gauss-Bonnet theorem
    • Chern-Weil homomorphism
  • Cartan connection
    • Cartan connection applications
    • Vierbein
    • Einstein-Cartan theory
  • Covariant derivative
  • Levi-Civita connection
  • Moving frame
  • Parallel transport
  • Torsion

Other

• Envelope (mathematics)
• Bäcklund transform