Differential geometry
ScienceWISE definitions
External resources
Incoming relations
- Curvature tensor is important in Differential geometry
- Monge-Ampère equation is used in Differential geometry
Outgoing relations
- Differential geometry is used in General relativity
Subcategories
Concepts
- 2 pi theorem
- Abel-Jacobi map
- Abstract differential geometry
- Adjoint bundle
- Affine connection
- Affine curvature
- Affine differential geometry
- Affine focal set
- Affine geometry of curves
- Affine Grassmannian
- Affine sphere
- Algebra bundle
- Algebraic vector bundle
- Almost complex manifold
- Almost flat manifold
- Almost symplectic manifold
- Ample line bundle
- Analytic torsion
- Anti de Sitter space
- Antimatroid
- Associated bundle
- Atiyah conjecture
- Banach bundle
- Banach manifold
- B-convex space
- Beauville-Laszlo theorem
- Beltrami's theorem
- Berger-Kazdan comparison theorem
- Berger's inequality for Einstein manifolds
- Berger's sphere
- Bernstein's problem
- Bertrand-Diquet-Puiseux theorem
- Birkhoff-Grothendieck theorem
- Bishop-Gromov inequality
- Bitangent
- Bochner identity
- Bochner's formula
- Bogomolov-Miyaoka-Yau inequality
- Bonnet theorem
- Bryant surface
- Bundle gerbe
- Bundle map
- Calabi conjecture
- Calabi-Yau spaces
- Calculus of moving surfaces
- Calibrated geometry
- Canonical bundle
- Carathéodory conjecture
- Carnot-Caratheodory metric
- Cartan connection
- Cartan formalism
- Cartan-Hadamard theorem
- Cartan-Karlhede algorithm
- Cartan's equivalence method
- Cayley's ruled cubic surface
- Center of curvature
- Characteristic class
- Cheeger constant
- Cheng's eigenvalue comparison theorem
- Chern class
- Chern-Simons form
- Chern-Weil homomorphism
- Chern-Weil theory
- Chordal problem
- Christoffel symbols
- Circle bundle
- Clairaut's relation
- Classifying space
- Clifford analysis
- Clifford bundle
- Closed geodesic
- Cocurvature
- Coframe
- Collapsing manifold
- Comparison theorem
- Concave set
- Conformal connection
- Conformal geometry
- Conformal Killing equation
- Conformally flat manifold
- Conformal map
- Conical combination
- Conjugate points
- Connection form
- Constant curvature
- Constraint counting
- Convex and concave polygons
- Convex curve
- Convex geometry
- Convex polytope
- Convex set
- Coordinate-induced basis
- Costa's minimal surface
- Cotangent bundle
- Cotton tensor
- Courant bracket
- Covariance and contravariance of vectors
- Covariant classical field theory
- Covariant derivative
- Covariant Hamiltonian field theory
- Covariant transformation
- Covering space
- Crofton formula
- Curvature form
- Curvature invariant
- Curvature of Riemannian manifolds
- Curved space
- Cut locus
- Darboux frame
- Darboux vector
- De Sitter invariant special relativity
- De Sitter-Schwarzschild metric
- De Sitter space
- Developable surface
- Diffeology
- Differentiable manifold
- Differential form of degree three
- Differential invariant
- Directional derivative
- Discrete differential geometry
- Double tangent bundle
- Dual bundle
- Dual cone and polar cone
- Dual curve
- Dykstra's projection algorithm
- Ehresmann connection
- Einstein manifold
- Elliptic complex
- Equiareal map
- Equichordal point problem
- Essential manifold
- Euler class
- Euler's theorem
- Exponential map
- Exterior bundle
- Exterior covariant derivative
- Extrinsic curvature
- Fenchel's theorem
- Fermi coordinates
- Fiber bundle
- Fiber bundle construction theorem
- Filling area conjecture
- Filling radius
- Finsler manifold
- First fundamental form
- First variation of area formula
- Fisher information metric
- Flat manifold
- Four-vertex theorem
- Frame bundle
- Frenet-Serret formulas
- Frobenius manifold
- Frobenius theorem
- Frölicher-Nijenhuis bracket
- Fundamental theorem of curves
- Fundamental theorem of Riemannian geometry
- G2 manifold
- G2-structure
- Gauge covariant derivative
- Gauss-Codazzi equations
- Gaussian curvature
- Gauss-Manin connection
- Gauss map
- Gauss's lemma
- General covariance
- Generalized flag variety
- Generalized Gauss-Bonnet theorem
- Geodesic convexity
- Geodesic curvature
- Geodesic deviation equation
- Geodesic manifold
- Geodesic map
- Geodesics as Hamiltonian flows
- Geometric flow
- Geometrization conjecture
- Gilbert-Johnson-Keerthi distance algorithm
- Grassmannian
- Gravitational instanton
- Gromov-Hausdorff convergence
- Gromov's compactness theorem
- Gromov's inequality for complex projective space
- Gromov's systolic inequality for essential manifolds
- Grothendieck connection
- G-structure
- Harmonic coordinates
- Harmonic map
- Hermitian connection
- Hermitian manifold
- Hermitian symmetric space
- Hilbert scheme
- Hilbert's theorem
- Hitchin-Thorpe inequality
- Hodge star
- Holomorphic vector bundle
- Holonomy
- Homological mirror symmetry
- Hopf conjecture
- Hopf-Rinow theorem
- Horizontal bundle
- Horrocks bundle
- Horrocks-Mumford bundle
- Hsiang-Lawson's conjecture
- Hyperbolic Space
- Hypercomplex manifold
- Hyperkähler manifold
- I-bundle
- Iitaka dimension
- Induced metric
- Integral curve
- Introduction to systolic geometry
- Inverse bundle
- Inverse mean curvature flow
- Involute
- Isometry
- Isoparametric manifold
- Isotropic manifold
- Iwasawa manifold
- Jacobi field
- Jet bundle
- Kähler-Einstein metric
- Kahler geometry
- Kähler manifold
- Kahler moduli space
- Kahler potential
- Kakutani's theorem
- Kappa-Minkowski spacetime
- Killing tensor
- Killing vector field
- Klee-Minty cube
- Klein geometry
- Kretschmann scalar
- Kulkarni-Nomizu product
- L² cohomology
- Lanczos tensor
- Laplace-Beltrami operator
- Leray-Hirsch theorem
- Levi-Civita connection
- Levi-Civita parallelogramoid
- Lichnerowicz formula
- Lie bracket of vector fields
- Lie groupoid
- Lie sphere geometry
- Line bundle
- Line element
- Liouville's equation
- Local coordinate system
- Loewner's torus inequality
- Mahler volume
- Manifold
- Margulis lemma
- Maurer-Cartan
- Maurer-Cartan form
- Mean curvature
- Mean curvature flow
- Menger curvature
- Metric bundle
- Metric connection
- Metric signature
- Metric tensor
- Meusnier's theorem
- Milnor fibration
- Minimal surface
- Minimal volume
- Minkowski addition
- Minkowski Portal Refinement
- Minkowski's theorem
- Morse theory
- Mostow rigidity theorem
- Multivector
- Musical isomorphism
- Myers's theorem
- Nadirashvili surface
- Nash embedding theorem
- Natural pseudodistance
- N-connected
- Nearly Kähler manifold
- Negative pedal curve
- Nijenhuis bracket
- Non-commutative space
- Non-convexity
- Nonholonomic system
- Non-metric connection
- Nonmetricity tensor
- Normal bundle
- Normal coordinates
- Nuts and bolts
- Oriented matroid
- Orthogonal symmetric Lie algebra
- Orthonormal frame
- Osculating circle
- Osculating plane
- Parabolic geometry
- Parallel transport
- Pedal curve
- Petrov classification
- Plücker embedding
- Poisson manifold
- Pontryagin class
- Prescribed Ricci curvature problem
- Prescribed scalar curvature problem
- Principal bundle
- Principal curvature
- Principal geodesic analysis
- Projective connection
- Projective differential geometry
- Projective vector field
- Proofs involving covariant derivatives
- Pseudogroup
- Pseudo-Riemannian manifold
- Pseudosphere
- Pullback bundle
- Pu's inequality
- Quaternion-Kähler manifold
- Quaternion-Kähler symmetric space
- Real projective space
- Recurrent tensor
- Reduction of the structure group
- Ricci decomposition
- Ricci-flat manifold
- Ricci flow
- Riemannian circle
- Riemannian connection on a surface
- Riemannian geometry
- Riemannian manifold
- Riemannian Penrose inequality
- Riemannian submanifold
- Riemannian submersion
- Rotating calipers
- Round function
- Ruled surface
- Ruppeiner geometry
- Sasakian manifold
- Scalar curvature
- Schild's ladder
- Schouten-Nijenhuis bracket
- Schouten tensor
- Schur's lemma
- Secondary vector bundle structure
- Second fundamental form
- Sectional curvature
- Segre class
- Seifert fiber space
- Seifert-Weber space
- Self-dual form
- Separating axis theorem
- Seshadri constant
- Sharafutdinov's retraction
- Sharp map
- Simply connected space
- Smooth coarea formula
- Solder form
- Soul theorem
- Space form
- Spectral geometry
- Sphere theorem
- Spherical 3-manifold
- Spin structure
- Splitting principle
- Splitting theorem
- Stable normal bundle
- Stiefel manifold
- Stiefel-Whitney class
- Subbundle
- Sub-riemannian geometry
- Support function
- Symmetric Lie group
- Symmetric space
- Symplectic manifold
- Symplectic space
- Synge's theorem
- Synthetic differential geometry
- Systoles of surfaces
- Systolic freedom
- Systolic geometry
- Tangent bundle
- Tangential angle
- Tangent indicatrix
- Tangent space
- Tango bundle
- Tautological bundle
- Tautological line bundle
- Taut submanifold
- Tempered dilatation structure
- Tensor bundle
- Tensor field
- Tetrad
- Theorema Egregium
- Thom space
- Thurston elliptization conjecture
- Todd class
- Toponogov's theorem
- Torsion of a curve
- Torsion tensor
- Tortuosity
- Torus bundle
- Total curvature
- Tractor bundle
- Transversality theorem
- Two-form
- Unit tangent bundle
- Universal bundle
- Vector field
- Vector flow
- Vector-valued differential form
- Vertical bundle
- Warped geometry
- Weakly symmetric space
- Weierstrass-Enneper parameterization
- Wente torus
- Weyl-Schouten theorem
- Weyl tensor
- Weyl transformation
- Wiedersehen pair
- Willmore conjecture
- Willmore energy
- Wirtinger inequality
- Yamabe flow
- Yamabe invariant
- Yamabe problem
- Zoll surface
Categorization
Mathematics (under construction)Synonyms
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