OpenDEM 1: 1 revision imported from :wikipedia:en:Template:Manifolds

2025-08-17T18:58:44Z

1 revision imported from wikipedia:en:Template:Manifolds

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wikipedia:en>SpiralSource: fixed major error

2025-06-10T21:15:18Z

fixed major error

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{{Navbox
| name = Manifolds
| title = [[Manifold]]s ([[Glossary of differential geometry and topology|Glossary]], [[List of manifolds|List]], [[:Category:Manifolds|Category]])
| state = {{{state|<noinclude>uncollapsed autocollapse expanded</noinclude><includeonly>autocollapse</includeonly>}}}

| image =
| bodyclass = hlist
| selected = {{{1}}}
| above =

| group1 = Basic concepts
| list1 =
* [[Topological manifold]]
** [[Atlas (topology)|Atlas]]
* [[Differentiable manifold|Differentiable/Smooth manifold]]
** [[Differential structure]]
** [[Smooth structure|Smooth atlas]]
* [[Submanifold]]
* [[Riemannian manifold]]
* [[Smoothness|Smooth map]]
* [[Submersion (mathematics)|Submersion]]
* [[Pushforward (differential)|Pushforward]]
* [[Tangent space]]
* [[Differential form]]
* [[Vector field]]

| group10 = Main results {{smaller|[[:Category:Theorems in differential geometry|(list)]]}}
| list10 =
* [[Atiyah–Singer index theorem|Atiyah–Singer index]]
* [[Darboux's theorem|Darboux's]]
* [[De Rham cohomology#De Rham's theorem|De Rham's]]
* [[Frobenius theorem (differential topology)|Frobenius]]
* [[Generalized Stokes theorem|Generalized Stokes]]
* [[Hopf–Rinow theorem|Hopf–Rinow]]
* [[Noether's theorem|Noether's]]
* [[Sard's theorem|Sard's]]
* [[Whitney embedding theorem|Whitney embedding]]

| group20 = [[Smoothness|Maps]]
| list20 =
* [[Differentiable curve|Curve]]
* [[Diffeomorphism]]
** [[Local diffeomorphism|Local]]
* [[Geodesic]]
* [[Exponential map (Riemannian geometry)|Exponential map]]
** [[Exponential map (Lie theory)|in Lie theory]]
* [[Foliation]]
* [[Immersion (mathematics)|Immersion]]
* [[Integral curve]]
* [[Lie derivative]]
* [[Section (fiber bundle)|Section]]
* [[Submersion (mathematics)|Submersion]]

| group30 = Types of<br />manifolds
| list30 =
* [[Closed manifold|Closed]]
* [[Collapsing manifold|Collapsing]]
* [[Complete manifold|Complete]]
* ([[Almost complex manifold|Almost]]) [[Complex manifold|Complex]]
* ([[Almost-contact manifold|Almost]]) [[Contact manifold|Contact]]
* [[Fibered manifold|Fibered]]
* [[Finsler manifold|Finsler]]
* ([[Almost flat manifold|Almost]]) [[Flat manifold|Flat]]
* [[G-structure on a manifold|G-structure]]
* [[Hadamard manifold|Hadamard]]
* [[Hermitian manifold|Hermitian]]
* [[Hyperbolic manifold|Hyperbolic]]
* [[Kähler manifold|Kähler]]
* [[Kenmotsu manifold|Kenmotsu]]
* [[Lie group]]
** [[Lie group–Lie algebra correspondence|Lie algebra]]
* [[Manifold with boundary]]
* [[Nilmanifold]]
* [[Orientability|Oriented]]
* [[Parallelizable manifold|Parallelizable]]
* [[Poisson manifold|Poisson]]
* [[Prime manifold|Prime]]
* [[Quaternionic manifold|Quaternionic]]
* [[Hypercomplex manifold|Hypercomplex]]
* ([[Pseudo-Riemannian manifold|Pseudo-]], [[Sub-Riemannian manifold|Sub-]]) [[Riemannian manifold|Riemannian]]
* [[Rizza manifold|Rizza]]
* [[Stein manifold|Stein]]
* ([[Almost symplectic manifold|Almost]]) [[Symplectic manifold|Symplectic]]
* [[Tame manifold|Tame]]

| group40 = [[Tensor]]s
| list40 = {{#invoke:Navbox|navbox|child

| group50 = Vectors
| list50 =
* [[Distribution (differential geometry)|Distribution]]
* [[Lie bracket of vector fields|Lie bracket]]
* [[Pushforward (differential)|Pushforward]]
* [[Tangent space]]
** [[Tangent bundle|bundle]]
* [[Torsion tensor|Torsion]]
* [[Vector field]]
* [[Vector flow]]

| group65 = Covectors
| list65 =
* [[Closed and exact differential forms|Closed/Exact]]
* [[Covariant derivative]]
* [[Cotangent space]]
** [[Cotangent bundle|bundle]]
* [[De Rham cohomology]]
* [[Differential form]]
** [[Vector-valued differential form|Vector-valued]]
* [[Exterior derivative]]
* [[Interior product]]
* [[Pullback (differential geometry)|Pullback]]
* [[Ricci curvature]]
** [[Ricci flow|flow]]
* [[Riemann curvature tensor]]
* [[Tensor field]]
** [[Tensor density|density]]
* [[Volume form]]
* [[Wedge product]]

| group75 = [[Fiber bundle|Bundles]]
| list75 =
* [[Adjoint bundle|Adjoint]]
* [[Affine bundle|Affine]]
* [[Associated bundle|Associated]]
* [[Cotangent bundle|Cotangent]]
* [[Dual bundle|Dual]]
* [[Fiber bundle|Fiber]]
* ([[Cofibration|Co-]]) [[Fibration]]
* [[Jet bundle|Jet]]
* [[Lie algebra bundle|Lie algebra]]
* ([[Stable normal bundle|Stable]]) [[Normal bundle|Normal]]
* [[Principal bundle|Principal]]
* [[Spinor bundle|Spinor]]
* [[Subbundle]]
* [[Tangent bundle|Tangent]]
* [[Tensor bundle|Tensor]]
* [[Vector bundle|Vector]]

| group85 = [[Connection (mathematics)|Connections]]
| list85 =
* [[Affine connection|Affine]]
* [[Cartan connection|Cartan]]
* [[Ehresmann connection|Ehresmann]]
* [[Connection form|Form]]
* [[Connection (fibred manifold)|Generalized]]
* [[Koszul connection|Koszul]]
* [[Levi-Civita connection|Levi-Civita]]
* [[Connection (principal bundle)|Principal]]
* [[Connection (vector bundle)|Vector]]
* [[Parallel transport]]

}}

| group90 = Related
| list90 =
* [[Classification of manifolds]]
* [[Gauge theory (mathematics)|Gauge theory]]
* [[History of manifolds and varieties|History]]
* [[Morse theory]]
* [[Moving frame]]
* [[Singularity theory]]

| group95 = Generalizations
| list95 =
* [[Banach manifold]]
* [[Diffeology]]
* [[Diffiety]]
* [[Fréchet manifold]]
* [[K-theory]]
* [[Orbifold]]
* [[Secondary calculus and cohomological physics|Secondary calculus]]
** [[Differential calculus over commutative algebras|over commutative algebras]]
* [[Sheaf (mathematics)|Sheaf]]
* [[Stratifold]]
* [[Supermanifold]]
* [[Stratified space]]

}}<noinclude>
{{Documentation
| content =
{{Collapsible option |statename=optional}}
}}
[[Category:Topology navigational boxes]]
</noinclude>

Template:Manifolds - Revision history

OpenDEM 1: 1 revision imported from :wikipedia:en:Template:Manifolds

wikipedia:en>SpiralSource: fixed major error