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Contact geometry

In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'. Equivalently, such a distribution may be given (at least locally) as the kernel of a differential one-form, and the non-integrability condition…

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Overview

Mathematical formulation

Examples

Contact transformation

Submanifolds

Vector fields

Relation with symplectic geometry

Topology

History

Applications

Introductions to contact geometry

Contact three-manifolds and Legendrian knots

Information on the history of contact geometry

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Map overview Semantic statistics

Contact geometry

Nodes150
Edges149
Triples93
Avg. degree1.99
Density0.013333
Components1

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Contact geometry

Top relations

related to history · 38
Contact geometry → Apollonius, Arnold, Barrow, Birkhäuser, Brief History, Cagliari, Christiaan Huygens, Concepts, Conference, Contact, Differential Geometry, Expo, Fac, Geiges, Hooke, Huygens, Isaac Barrow, Isaac Newton, ISBN, Legendre
related to Introductions to contact geometry · 33
Contact geometry → Aebischer, An Introduction, Arnold, Berührungstransformationen, Birkhäuser, Cambridge University Press, Classical Mechanics, Contact Topology, CS1, Etnyre, Geiges, Geometrie, Georg Wilhelm, German, Hansjörg, Introductory, ISBN, Leipzig, Lie, Mathematical Methods
has application · 9
Contact geometry → Contact, It, Kronheimer, Lenhard Ng, Like, Michael Hutchings, Mrowka, Stein, Yakov Eliashberg
related to Partial differential equations · 5
Contact geometry → In, Legendrian, PDE, Sophus Lie's, The
related to Relation with symplectic geometry · 3
Contact geometry → Because, Concretely, There
is a · 2
Contact geometry → stable distribution, study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability

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Important terminology

contact displaystyle mathbb manifold structure alpha form symplectic legendrian given vector field geometry omega infinitesimal reeb standard bundle distribution defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Contact geometryis astudy of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability0.90text
Contact geometryis astable distribution0.90text
symplectic field theory andinstance ofThe dynamics of the Reeb field can be used to study the structure of the contact manifold or even the underlying manifold using techniques of Floer homology0.80text
in three dimensionsinstance ofThe dynamics of the Reeb field can be used to study the structure of the contact manifold or even the underlying manifold using techniques of Floer homology0.80text
embedded contact homologyinstance ofThe dynamics of the Reeb field can be used to study the structure of the contact manifold or even the underlying manifold using techniques of Floer homology0.80text
Contact geometryhas applicationLike0.60section
Contact geometryhas applicationContact0.60section
Contact geometryhas applicationKronheimer0.60section
Contact geometryhas applicationMrowka0.60section
Contact geometryhas applicationMichael Hutchings0.60section
Contact geometryhas applicationLenhard Ng0.60section
Contact geometryhas applicationIt0.60section

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