List of differential geometry topics
From Wikipedia, the free encyclopedia
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics.
Differential geometry of curves and surfaces
Foundations
Calculus on manifolds
See also multivariable calculus, list of multivariable calculus topics
Differential topology
Fiber bundles
Fundamental structures
Riemannian geometry
Fundamental notions
Non-Euclidean geometry
Geodesic
Symmetric spaces (and related topics)
Riemannian submanifolds
Curvature of Riemannian manifolds
Theorems in Riemannian geometry
- Gauss–Bonnet theorem
- Hopf–Rinow theorem
- Cartan–Hadamard theorem
- Myers theorem
- Rauch comparison theorem
- Morse index theorem
- Synge theorem
- Weinstein theorem
- Toponogov theorem
- Sphere theorem
- Hodge theory
- Uniformization theorem
- Yamabe problem
Isometry
Laplace–Beltrami operator
Formulas and other tools
Related structures
Lie groups
Connections
Complex manifolds
- Riemann surface
- Complex projective space
- Kähler manifold
- Dolbeault operator
- CR manifold
- Stein manifold
- Almost complex structure
- Hermitian manifold
- Newlander–Nirenberg theorem
- Generalized complex manifold
- Calabi–Yau manifold
- Hyperkähler manifold
- K3 surface
- hypercomplex manifold
- Quaternion-Kähler manifold
Symplectic geometry
Conformal geometry
Index theory
Homogeneous spaces
Systolic geometry
- Loewner's torus inequality
- Pu's inequality
- Gromov's inequality for complex projective space
- Wirtinger inequality (2-forms)
- Gromov's systolic inequality for essential manifolds
- Essential manifold
- Filling radius
- Filling area conjecture
- Bolza surface
- First Hurwitz triplet
- Hermite constant
- Systoles of surfaces
- Systolic freedom
- Systolic category