In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It arises naturally from the study of the theory of differential equations. Differential geometry is the study of geometry using calculus. These fields are adjacent, and have many applications in physics, notably in the theory of relativity. Together they make up the geometric theory of differentiable manifolds - which can also be studied directly from the point of view of dynamical systems.

Subcategories

There are 7 subcategories to this category.

Complex manifolds D Differential topology

F Fiber bundles L Lie groups R Riemannian geometry

S Surfaces T Tensors

Articles in category "Differential geometry"

There are 94 articles in this category.

Affine connection Almost complex manifold Associated bundle Atiyah-Singer index theorem B Bäcklund transform C Calabi-Yau manifold Cartan connection Cartan connection applications Caustic (mathematics) Characteristic class Chern class Chern-Simons form Chern-Weil homomorphism Closed and exact differential forms Conformal geometry Connection (mathematics) Connection form Contravariant Covariant Covariant derivative Curvature Curvature form Curves in differential geometry D Darboux vector De Rham cohomology Differential geometry and topology Differential geometry of curves Directional derivative E Einstein tensor Embedding Envelope (mathematics)

E cont. Evolute F Finsler geometry Fisher information metric Flag manifold Frenet-Serret formulas Frobenius theorem Fundamental theorem of curves G G-structure G2 manifold Gauge theory Gauss map Generalized Gauss-Bonnet theorem Glossary of differential geometry and topology Grassmannian H Hermitian metric Holonomic Holonomy Hopf bundle Hyperkähler manifold I Induced metric Instanton K K3 surface Kähler manifold L List of differential geometry topics M Manifold Mean curvature Metric signature Minimal surface Monodromy Moving frame N Nonmetricity tensor O Orientable manifold

P P-vector Poisson manifold Pontryagin class Principal bundle Projective differential geometry Pseudogroup Pseudosphere Pullback Push forward R Real projective space Riemannian symmetric space S Schwarz-Ahlfors-Pick theorem Second fundamental form Sine-Gordon equation Singularity theory Sphere Spinor bundle Stiefel manifold Swan's theorem Symplectic manifold Symplectic space T Tangent Tangent space Taut foliation Taut submanifold Tensor field Tetrad (index notation) Theorema Egregium Torsion U Upper half plane W Weyl transformation