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2016, Second edition., Graduate studies in mathematics, ISBN 1470409860, Volume 175., xviii, 453 pages

Book

2017, Graduate studies in mathematics, ISBN 9781470429522, Volume 178, xvi, 414 pages

Lorentz metrics, indefinite metrics | Classical differential geometry | Vector analysis | Differential geometry | Global analysis, analysis on manifolds | Local differential geometry | Surfaces in Euclidean space | Differential forms | Noncompact transformation groups | Exterior differential systems (Cartan theory) | Projective differential geometry | Frames (Vector analysis) | Homogeneous spaces | Geometry, Differential | Topological groups, Lie groups | Affine differential geometry | Local submanifolds | General theory of differentiable manifolds | Mathematical physics | Exterior differential systems | Differential invariants (local theory), geometric objects | Curves in Euclidean space

Book

2003, Graduate studies in mathematics, ISBN 9780821833759, Volume 61, xiv, 378

Book

1963, 75 leaves

Book

Differential geometry and its applications, ISSN 0926-2245, 12/2016, Volume 49, pp. 351 - 371

The k-Dirac operator is a first order differential operator which is natural to a particular class of parabolic geometries which include the Lie contact structures...

Weighted jets | Cartan–Kähler theorem | Initial value problem | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematics - Differential Geometry

Weighted jets | Cartan–Kähler theorem | Initial value problem | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Mathematics - Differential Geometry

Journal Article

1991, Mathematical Sciences Research Institute publications, Volume 18, vii, 475 p. --

Book

The Asian journal of mathematics, ISSN 1093-6106, 2011, Volume 15, Issue 4, pp. 521 - 538

This article uses Cartan-Kahler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps...

Conservation laws | Generalized isometric embeddings of vector bundles | Cartan-K̈ahler theory | Conservation laws for energy-momentum tensors | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Cartan–Kähler theory | 32C22 | 37K05 | 58A15 | exterior differential systems | generalized isometric embeddings of vector bundles | conservation laws for energy-momentum tensors

Conservation laws | Generalized isometric embeddings of vector bundles | Cartan-K̈ahler theory | Conservation laws for energy-momentum tensors | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Cartan–Kähler theory | 32C22 | 37K05 | 58A15 | exterior differential systems | generalized isometric embeddings of vector bundles | conservation laws for energy-momentum tensors

Journal Article

The European physical journal. C, Particles and fields, ISSN 1434-6044, 1/2013, Volume 73, Issue 1, pp. 1 - 5

Einstein–Cartan theory is formulated in (1+2) dimensions using the algebra of exterior differential forms...

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | Physical Sciences | Physics, Particles & Fields | Science & Technology | Gravitation | Algebra | Condensates | Mathematical analysis | Exteriors | Exact solutions | Variational principles | Torsion

Nuclear Physics, Heavy Ions, Hadrons | Measurement Science and Instrumentation | Nuclear Energy | Quantum Field Theories, String Theory | Physics | Elementary Particles, Quantum Field Theory | Astronomy, Astrophysics and Cosmology | Physical Sciences | Physics, Particles & Fields | Science & Technology | Gravitation | Algebra | Condensates | Mathematical analysis | Exteriors | Exact solutions | Variational principles | Torsion

Journal Article

Acta applicandae mathematicae, ISSN 0167-8019, 5/2005, Volume 87, Issue 1, pp. 147 - 164

We give an elementary introduction to exterior differential systems and the Cartan...

Cartan–Kähler theory | Mathematical and Computational Physics | Mechanics | Mathematics, general | Mathematics | exterior differential systems | Computer Science, general | Statistical Physics | Cartan-Kähler theory | Exterior differential systems | Studies | Mathematical analysis

Cartan–Kähler theory | Mathematical and Computational Physics | Mechanics | Mathematics, general | Mathematics | exterior differential systems | Computer Science, general | Statistical Physics | Cartan-Kähler theory | Exterior differential systems | Studies | Mathematical analysis

Journal Article

Acta applicandae mathematicae, ISSN 0167-8019, 05/2005, Volume 87, Issue 1-3, pp. 147 - 164

Journal Article

The Asian journal of mathematics, ISSN 1093-6106, 2007, Volume 11, Issue 4, pp. 699 - 726

We analyze the geometry of sub-Finsler Engel manifolds, computing a complete set of local invariants for a large class of these manifolds. We derive geodesic...

Engel manifolds | Sub-Finsler geometry | Optimal control theory | Cartan's method of equivalence | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | 53B40 | 58A15 | 53C10 | 53C17 | optimal control theory | exterior differential systems | 49J15 | Cartan’s method of equivalence

Engel manifolds | Sub-Finsler geometry | Optimal control theory | Cartan's method of equivalence | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | 53B40 | 58A15 | 53C10 | 53C17 | optimal control theory | exterior differential systems | 49J15 | Cartan’s method of equivalence

Journal Article

Symmetry, integrability and geometry, methods and applications, ISSN 1815-0659, 2008, Volume 4, p. 063

Exterior differential systems are given, and their Cartan characters calculated, for Maxwell and SU(2...

Su-Yang-Mills equations | Maxwell equations | Cartan characters | Exterior differential systems | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | exterior differential systems | SU-Yang-Mills equations

Su-Yang-Mills equations | Maxwell equations | Cartan characters | Exterior differential systems | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | exterior differential systems | SU-Yang-Mills equations

Journal Article

2018, ISBN 012814274X

With this chapter, we come back to Élie Cartan's work by discussing his fundamental contributions in the realm of the integration theory of general systems of Pfaffian equations...

Exterior calculus | Cartan's existence theorem | Exterior derivative | Pfaffian equation | Bilinear covariant

Exterior calculus | Cartan's existence theorem | Exterior derivative | Pfaffian equation | Bilinear covariant

Book Chapter

Acta applicandae mathematicae, ISSN 0167-8019, 10/2007, Volume 99, Issue 1, pp. 97 - 116

Based on the exterior differential calculus, we define the exterior difference system on the hypercubic lattice...

Exterior difference system | 52C99 | Mathematical and Computational Physics | Mathematics | Discrete retraction theorem | Noncommutative calculus | 81T75 | Discrete Frobenius theorem | Mechanics | Mathematics, general | Discrete Cartan–Kähler theorem | Computer Science, general | Statistical Physics | 03G10 | Discrete Cartan-Kähler theorem | Physical Sciences | Mathematics, Applied | Science & Technology | Studies | Calculus | Mathematical models | Theory | Differential equations | Differential calculus | Operators | Theorems | Mathematical analysis | Exteriors | Lattices | Derivatives | Contracts | Construction contracts

Exterior difference system | 52C99 | Mathematical and Computational Physics | Mathematics | Discrete retraction theorem | Noncommutative calculus | 81T75 | Discrete Frobenius theorem | Mechanics | Mathematics, general | Discrete Cartan–Kähler theorem | Computer Science, general | Statistical Physics | 03G10 | Discrete Cartan-Kähler theorem | Physical Sciences | Mathematics, Applied | Science & Technology | Studies | Calculus | Mathematical models | Theory | Differential equations | Differential calculus | Operators | Theorems | Mathematical analysis | Exteriors | Lattices | Derivatives | Contracts | Construction contracts

Journal Article

Symmetry, integrability and geometry, methods and applications, ISSN 1815-0659, 2009, Volume 5, p. 095

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e...

Affine distributions | Cartan's method of equivalence | Control theory | Exterior differential systems | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | exterior differential systems | affine distributions | control theory

Affine distributions | Cartan's method of equivalence | Control theory | Exterior differential systems | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | exterior differential systems | affine distributions | control theory

Journal Article

Mathematics and mechanics of solids, ISSN 1081-2865, 9/2013, Volume 18, Issue 7, pp. 738 - 744

.... We set down a system of exterior differential equations which when solved render the totality of the uniform references that may be healed by a given symmetry group...

exterior forms | exterior differential equations | Cartan's equations of structure | Dislocations | Mathematics, Interdisciplinary Applications | Physical Sciences | Materials Science | Technology | Materials Science, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Usage | Numerical analysis | Analysis | Differential equations | Elasticity | Mechanical properties | Solids | Methods | Mathematical analysis | Exteriors | Group theory | Inhomogeneity | Calculus | Symmetry

exterior forms | exterior differential equations | Cartan's equations of structure | Dislocations | Mathematics, Interdisciplinary Applications | Physical Sciences | Materials Science | Technology | Materials Science, Multidisciplinary | Mechanics | Mathematics | Science & Technology | Usage | Numerical analysis | Analysis | Differential equations | Elasticity | Mechanical properties | Solids | Methods | Mathematical analysis | Exteriors | Group theory | Inhomogeneity | Calculus | Symmetry

Journal Article

Symmetry, integrability and geometry, methods and applications, ISSN 1815-0659, 01/2009, Volume 5, p. 087

This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS...

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | variation of Hodge structure | Chern classes | Hodge conjecture | Noether-Lefschetz locus | integral manifold | exterior differential systems | Pfaffian system | characteristic cohomology | Cartan-Kähler theorem | period domain

Physical Sciences | Physics | Physics, Mathematical | Science & Technology | variation of Hodge structure | Chern classes | Hodge conjecture | Noether-Lefschetz locus | integral manifold | exterior differential systems | Pfaffian system | characteristic cohomology | Cartan-Kähler theorem | period domain

Journal Article

Differential geometry and its applications, ISSN 0926-2245, 2006, Volume 24, Issue 6, pp. 628 - 651

We define the notion of
sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory...

Sub-Finsler geometry | Optimal control theory | Cartan's method of equivalence | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Sub-Finsler geometry | Optimal control theory | Cartan's method of equivalence | Exterior differential systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Acta applicandae mathematicae, ISSN 0167-8019, 2/2007, Volume 95, Issue 3, pp. 223 - 231

The method of Cartan is reviewed by applying it to the classical Korteweg-de Vries equation...

35C05 | 32A25 | Mathematical and Computational Physics | Solitons | Mathematics | Exterior differential system | Cartan prolongation | Generalized KdV equation | Mechanics | Mathematics, general | 35A30 | Computer Science, general | Statistical Physics | Physical Sciences | Mathematics, Applied | Science & Technology | Studies | Mathematical analysis | Integral calculus | Transformations (mathematics) | Exteriors | Prolongation | Differential equations

35C05 | 32A25 | Mathematical and Computational Physics | Solitons | Mathematics | Exterior differential system | Cartan prolongation | Generalized KdV equation | Mechanics | Mathematics, general | 35A30 | Computer Science, general | Statistical Physics | Physical Sciences | Mathematics, Applied | Science & Technology | Studies | Mathematical analysis | Integral calculus | Transformations (mathematics) | Exteriors | Prolongation | Differential equations

Journal Article

Foundations of computational mathematics, ISSN 1615-3375, 4/2011, Volume 11, Issue 2, pp. 131 - 149

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms...

Economics general | Discrete Lie derivative | 65M08 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Hyperbolic PDEs | Numerical Analysis | 35Q35 | Discrete differential forms | Math Applications in Computer Science | Applications of Mathematics | 51P05 | Computer Science, general | Discrete contraction | Finite-volume methods | Physical Sciences | Technology | Computer Science | Computer Science, Theory & Methods | Mathematics, Applied | Science & Technology | Numerical analysis | Conservation laws | Operators | Foundations | Advection | Approximation | Exteriors | Scalars | Mathematical models | Derivatives

Economics general | Discrete Lie derivative | 65M08 | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Hyperbolic PDEs | Numerical Analysis | 35Q35 | Discrete differential forms | Math Applications in Computer Science | Applications of Mathematics | 51P05 | Computer Science, general | Discrete contraction | Finite-volume methods | Physical Sciences | Technology | Computer Science | Computer Science, Theory & Methods | Mathematics, Applied | Science & Technology | Numerical analysis | Conservation laws | Operators | Foundations | Advection | Approximation | Exteriors | Scalars | Mathematical models | Derivatives

Journal Article

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