List of differential geometry topics
(Redirected from Outline of differential geometry)
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 edit
Differential geometry of curves edit
- List of curves topics
- Frenet–Serret formulas
- Curves in differential geometry
- Line element
- Curvature
- Radius of curvature
- Osculating circle
- Curve
- Fenchel's theorem
Differential geometry of surfaces edit
Foundations edit
Calculus on manifolds edit
See also multivariable calculus, list of multivariable calculus topics
Differential topology edit
- Diffeomorphism
- Orientability
- characteristic class
- differentiable map
- Critical value
- Lie derivative
- Hairy ball theorem
- Poincaré–Hopf theorem
- Stokes' theorem
- De Rham cohomology
- Sphere eversion
- Frobenius theorem (differential topology)
Fiber bundles edit
Fundamental structures edit
Riemannian geometry edit
Fundamental notions edit
Non-Euclidean geometry edit
Geodesic edit
- Prime geodesic
- Geodesic flow
- Exponential map (Lie theory)
- Exponential map (Riemannian geometry)
- Injectivity radius
- Geodesic deviation equation
edit
Riemannian submanifolds edit
- Gauss–Codazzi equations
- Darboux frame
- Hypersurface
- Induced metric
- Nash embedding theorem
- minimal surface
- Hsiang–Lawson's conjecture
Curvature of Riemannian manifolds edit
- Theorema Egregium
- Gauss–Bonnet theorem
- Gauss map
- Second fundamental form
- Curvature form
- Riemann curvature tensor
- Geodesic curvature
- Scalar curvature
- Sectional curvature
- Ricci curvature, Ricci flat
- Ricci decomposition
- Ricci flow
- Einstein manifold
- Holonomy
Theorems in Riemannian geometry edit
- 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 edit
Laplace–Beltrami operator edit
Formulas and other tools edit
Related structures edit
Lie groups edit
Connections edit
Complex manifolds edit
- 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 edit
Conformal geometry edit
Index theory edit
Homogeneous spaces edit
Systolic geometry edit
- 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