Mediterranean Journal of Mathematics, ISSN 1660-5446, 2/2017, Volume 14, Issue 1, pp. 1 - 17

The tangent bundle $$T^kM$$ T k M of order k, of a smooth Banach manifold M consists of all equivalent classes of curves that agree up to their accelerations of order k...

Lagrangians | connection map | 58A05 | 58B20 | linear connection | Mathematics, general | Mathematics | Fréchet manifold | Banach manifold | higher order tangent bundle | lifting of Riemannian metrics | MATHEMATICS, APPLIED | SPACES | DIFFERENTIAL-EQUATIONS | Frechet manifold | CONNECTIONS | MATHEMATICS | MANIFOLDS | Mathematics - Differential Geometry

Lagrangians | connection map | 58A05 | 58B20 | linear connection | Mathematics, general | Mathematics | Fréchet manifold | Banach manifold | higher order tangent bundle | lifting of Riemannian metrics | MATHEMATICS, APPLIED | SPACES | DIFFERENTIAL-EQUATIONS | Frechet manifold | CONNECTIONS | MATHEMATICS | MANIFOLDS | Mathematics - Differential Geometry

Journal Article

Advances in Geometry, ISSN 1615-715X, 03/2017, Volume 17, Issue 2, pp. 175 - 189

The tangent bundle of order of a smooth Banach manifold consists of all equivalence classes of curves that agree up to their accelerations of order...

connection map | Secondary 58A05 | linear connection | Primary 58B20 | Hilbert manifold | related connection | Fréchet manifold | Banach manifold | higher order tangent bundle | lifting of Riemannian metrics | MATHEMATICS | MANIFOLDS | Frechet manifold | CONNECTIONS | Mathematics - Differential Geometry

connection map | Secondary 58A05 | linear connection | Primary 58B20 | Hilbert manifold | related connection | Fréchet manifold | Banach manifold | higher order tangent bundle | lifting of Riemannian metrics | MATHEMATICS | MANIFOLDS | Frechet manifold | CONNECTIONS | Mathematics - Differential Geometry

Journal Article

Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica, ISSN 0365-1029, 07/2014, Volume 68, Issue 2, pp. 59 - 64

...,-) between the tangent TM and the cotangent T[[low *]] M bundles of M. In the present note, we generalize this isomorphism to the one T[(r)]M [congruent with] T[r[low...

Manifolds | Tangents | Maps | Mathematical analysis | Isomorphism | Vectors (mathematics) | Bundles | Preserving

Manifolds | Tangents | Maps | Mathematical analysis | Isomorphism | Vectors (mathematics) | Bundles | Preserving

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2017, Volume 41, Issue 4, pp. 854 - 868

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle...

Double vector bundle | Canonical involution | Tangent bundle of higher order | Second order jets | Double jet bundle | MATHEMATICS | second order jets | double vector bundle | canonical involution | tangent bundle of higher order

Double vector bundle | Canonical involution | Tangent bundle of higher order | Second order jets | Double jet bundle | MATHEMATICS | second order jets | double vector bundle | canonical involution | tangent bundle of higher order

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 5/2014, Volume 11, Issue 2, pp. 799 - 811

...) the lifted foliation $${{\mathcal{F}}^{r}}$$ F r on the r-transverse bundle $${\nu^{r}{\mathcal{F}}}$$ ν r F is riemannian for an r...

(Higher order) Transverse bundle | 53C12 | Riemannian foliation | 70H50 | Mathematics, general | Transverse lagrangian | Mathematics | 53C60 | Lifted foliation | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | TANGENT BUNDLES | LAGRANGIANS

(Higher order) Transverse bundle | 53C12 | Riemannian foliation | 70H50 | Mathematics, general | Transverse lagrangian | Mathematics | 53C60 | Lifted foliation | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | TANGENT BUNDLES | LAGRANGIANS

Journal Article

Archivum Mathematicum, ISSN 0044-8753, 2014, Volume 50, Issue 2, pp. 115 - 130

Journal Article

Journal of Geometric Mechanics, ISSN 1941-4889, 2014, Volume 6, Issue 1, pp. 99 - 120

We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle...

Variational calculus | Geometric mechanics | Graded bundles | Higher tangent bundles | Integration by parts | Higher-order Euler-Lagrange equations | MATHEMATICS, APPLIED | variational calculus | higher-order Euler-Lagrange equations | graded bundles | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN SUBMANIFOLDS | MECHANICS | geometric mechanics | DYNAMICS | SYSTEMS | integration by parts

Variational calculus | Geometric mechanics | Graded bundles | Higher tangent bundles | Integration by parts | Higher-order Euler-Lagrange equations | MATHEMATICS, APPLIED | variational calculus | higher-order Euler-Lagrange equations | graded bundles | EQUATIONS | PHYSICS, MATHEMATICAL | LAGRANGIAN SUBMANIFOLDS | MECHANICS | geometric mechanics | DYNAMICS | SYSTEMS | integration by parts

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 2019, Volume 142, pp. 254 - 273

Pre-Courant algebroids are ‘Courant algebroids’ without the Jacobi identity for the Courant–Dorfman bracket. We examine the corresponding supermanifold...

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Q-manifolds | Supermanifolds | Courant algebroids | VB-Courant algebroids | Cochain complex | TANGENT LIFTS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL | MATHEMATICS | DOUBLE LIE ALGEBROIDS | DIRAC STRUCTURES | GRADED BUNDLES | MANIFOLDS | GEOMETRY

Journal Article

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 7/2014, Volume 35, Issue 3, pp. 264 - 280

The second order tangent bundle T 2 M of a smooth manifold M carries a natural structure of a smooth manifold over the algebra D 2 of truncated polynomials of degree two in one variable, which gives...

Geometry | Algebra | Second order tangent bundle | higher order connection | Analysis | frame bundle | Weil bundle | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | higher order tangent bundle | Mathematical Logic and Foundations

Geometry | Algebra | Second order tangent bundle | higher order connection | Analysis | frame bundle | Weil bundle | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | higher order tangent bundle | Mathematical Logic and Foundations

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 12/2011, Volume 42, Issue 4, pp. 579 - 606

...-Poisson reduction is also studied in detail. Keywords: variational principle, symmetry, connection, Poisson brackets, higher order tangent bundle, Lie-Poisson...

37J15 | Theoretical, Mathematical and Computational Physics | Poisson brackets | Mathematics | Hamilton-Poincaré equations | Lagrange-Poincaré equations | Euler-Poincaré equations | 70H25 | variational principle | 70H30 | symmetry | Lie-Poisson reduction | Euler-Lagrange equations | 70H50 | Mathematics, general | connection | higher order tangent bundle | Mathematical Physics | General Mathematics | Physics

37J15 | Theoretical, Mathematical and Computational Physics | Poisson brackets | Mathematics | Hamilton-Poincaré equations | Lagrange-Poincaré equations | Euler-Poincaré equations | 70H25 | variational principle | 70H30 | symmetry | Lie-Poisson reduction | Euler-Lagrange equations | 70H50 | Mathematics, general | connection | higher order tangent bundle | Mathematical Physics | General Mathematics | Physics

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 11/2016, Volume 12

We construct the full linearisation functor which takes a graded bundle of degree k...

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Polarisation | Supermanifolds | N-manifolds | Graded manifolds | K-fold vector bundles | supermani-folds | k-fold vector bundles | HIGHER-ORDER | POISSON | polarisation | LIE ALGEBROIDS | graded manifolds | Q-MANIFOLDS | HIGHER ANALOGS | PHYSICS, MATHEMATICAL

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 1/2009, Volume 158, Issue 1, pp. 61 - 81

.... We show that the phase bundle, i.e., the image of the Legendre transformation, is a submanifold of a certain cotangent bundle, and this submanifold is always odd-dimensional in this construction...

Nambu bracket | Mathematical and Computational Physics | Applications of Mathematics | higher-order tangent bundle | Physics | Hamiltonian formalism | reparameterization invariance | Higher-order tangent bundle | Reparameterization invariance | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Nambu bracket | Mathematical and Computational Physics | Applications of Mathematics | higher-order tangent bundle | Physics | Hamiltonian formalism | reparameterization invariance | Higher-order tangent bundle | Reparameterization invariance | DIMENSIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2015, Volume 48, Issue 20, pp. 1 - 32

In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids...

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Journal Article

Journal of Geometric Mechanics, ISSN 1941-4889, 12/2014, Volume 6, Issue 4, pp. 451 - 478

.... Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems...

Pontryagin's bundle | Skinner-rusk formalism | Higher-order tangent bundles | Optimal control of mechanical systems | Lie groups | MATHEMATICS, APPLIED | higher-order tangent bundles | optimal control of mechanical systems | LAGRANGIAN SYSTEMS | EQUATIONS | FLATNESS | PHYSICS, MATHEMATICAL | Skinner-Rusk formalism | EQUIVALENCE | GENERALIZED HAMILTONIAN-DYNAMICS | OPTIMAL ATTITUDE-CONTROL

Pontryagin's bundle | Skinner-rusk formalism | Higher-order tangent bundles | Optimal control of mechanical systems | Lie groups | MATHEMATICS, APPLIED | higher-order tangent bundles | optimal control of mechanical systems | LAGRANGIAN SYSTEMS | EQUATIONS | FLATNESS | PHYSICS, MATHEMATICAL | Skinner-Rusk formalism | EQUIVALENCE | GENERALIZED HAMILTONIAN-DYNAMICS | OPTIMAL ATTITUDE-CONTROL

Journal Article

15.
Full Text
Remarks on the behaviour of higher-order derivations on the gluing of differential spaces

Czechoslovak Mathematical Journal, ISSN 0011-4642, 12/2015, Volume 65, Issue 4, pp. 1137 - 1154

.... Therefore it is important to introduce a more general concept. In this paper, in particular, the behaviour of k th order tangent spaces, their dimensions...

higher-order differential geometry | Ordinary Differential Equations | gluing of differential space | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | Sikorski differential space | 58A40 | MATHEMATICS | FIELDS | REDUCTION | DE-RHAM COHOMOLOGY | SINGULARITIES | TANGENT-BUNDLES | CONNECTIONS

higher-order differential geometry | Ordinary Differential Equations | gluing of differential space | Analysis | Convex and Discrete Geometry | Mathematics, general | Mathematics | Mathematical Modeling and Industrial Mathematics | Sikorski differential space | 58A40 | MATHEMATICS | FIELDS | REDUCTION | DE-RHAM COHOMOLOGY | SINGULARITIES | TANGENT-BUNDLES | CONNECTIONS

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle...

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

CLASSICAL PSEUDOGROUPS | QUANTUM | PHYSICS, MATHEMATICAL | almost-Lie algebroid | variational principle | graded bundle | LAGRANGIAN SUBMANIFOLDS | MECHANICS | graded manifold | higher algebroid | vector bundle comorphism | GRADED BUNDLES | DYNAMICS | Q-MANIFOLDS | DUALITY | VARIATIONAL-PROBLEMS | algebroid lift | Bundling | Axioms

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 9/2015, Volume 2015, Issue 9, pp. 1 - 21

.... Introducing a background R-symmetry field strength R, and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m 1α + m 2 β + m 3γ, where the α...

Anomalies in Field and String Theories | Quantum Physics | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MATTER | F-THEORY | ANOMALIES | INSTANTONS | DYNAMICS | BRANES | PHYSICS, PARTICLES & FIELDS | Iridium base alloys | Field strength | Tangents | Mathematical analysis | Classification | Polynomials | Density | Anomalies

Anomalies in Field and String Theories | Quantum Physics | Field Theories in Higher Dimensions | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MATTER | F-THEORY | ANOMALIES | INSTANTONS | DYNAMICS | BRANES | PHYSICS, PARTICLES & FIELDS | Iridium base alloys | Field strength | Tangents | Mathematical analysis | Classification | Polynomials | Density | Anomalies

Journal Article

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, ISSN 1678-7544, 12/2011, Volume 42, Issue 4, pp. 579 - 606

Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for...

MATHEMATICS | variational principle | CLASSICAL PARTICLE | Hamilton-Poincare equations | symmetry | Poisson brackets | Lie-Poisson reduction | Euler-Lagrange equations | connection | higher order tangent bundle | Lagrange-Poincare equations | Euler-Poincare equations

MATHEMATICS | variational principle | CLASSICAL PARTICLE | Hamilton-Poincare equations | symmetry | Poisson brackets | Lie-Poisson reduction | Euler-Lagrange equations | connection | higher order tangent bundle | Lagrange-Poincare equations | Euler-Poincare equations

Journal Article

General relativity and gravitation, ISSN 1572-9532, 2010, Volume 43, Issue 9, pp. 2335 - 2392

.... Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a ‘tangent 2-group...

Category | Theoretical, Mathematical and Computational Physics | 2-group | Quantum Physics | String | Physics | Astronomy, Astrophysics and Cosmology | Gerbe | Higher gauge theory | Cosmology | 2-category | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | BUNDLE GERBES | PARALLEL TRANSPORT | PHYSICS, MULTIDISCIPLINARY | CONNECTIONS | DIFFERENTIAL GEOMETRY | BF THEORY | FEYNMAN DIAGRAMS | ASTRONOMY & ASTROPHYSICS | LINE BUNDLES | LOOP-SPACES | DEGREE-4 CHARACTERISTIC CLASSES | HIDDEN QUANTUM-GRAVITY | PHYSICS, PARTICLES & FIELDS

Category | Theoretical, Mathematical and Computational Physics | 2-group | Quantum Physics | String | Physics | Astronomy, Astrophysics and Cosmology | Gerbe | Higher gauge theory | Cosmology | 2-category | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | BUNDLE GERBES | PARALLEL TRANSPORT | PHYSICS, MULTIDISCIPLINARY | CONNECTIONS | DIFFERENTIAL GEOMETRY | BF THEORY | FEYNMAN DIAGRAMS | ASTRONOMY & ASTROPHYSICS | LINE BUNDLES | LOOP-SPACES | DEGREE-4 CHARACTERISTIC CLASSES | HIDDEN QUANTUM-GRAVITY | PHYSICS, PARTICLES & FIELDS

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 19

.... Systems defined in tangent bundles, Lie algebras, principal bundles, reduced systems, and constrained are included in such description...

37J15 | 70H50 | 53D05 | Mathematics, general | Mathematics | Lagrangian submanifolds | Lagrangian mechanics | Secondary 70H03 | Primary 53D12 | Mechanics on Lie algebroids | Higher order mechanics | 53D17 | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | TULCZYJEWS TRIPLET | VARIATIONAL-PROBLEMS | Algebra

37J15 | 70H50 | 53D05 | Mathematics, general | Mathematics | Lagrangian submanifolds | Lagrangian mechanics | Secondary 70H03 | Primary 53D12 | Mechanics on Lie algebroids | Higher order mechanics | 53D17 | MATHEMATICS | MATHEMATICS, APPLIED | SUBMANIFOLDS | TULCZYJEWS TRIPLET | VARIATIONAL-PROBLEMS | Algebra

Journal Article

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