Some Canonical Structures of Cartan Planes in Jet Spaces and Applications

Here we consider the problem of Whitney stratifying some very simple jet spaces. This type of problem has also been considered by Lander, Bedford and Gibson, (see (7), (1), (2)). Following Bedford and Gibson, we shall consider complex jet spaces.

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Jet spaces in modern Hamiltonian biomechanics

Open Physics ◽

10.2478/s11534-010-0024-x ◽

2010 ◽

Vol 8 (6) ◽

Cited By ~ 1

Author(s):

Tijana Ivancevic ◽

Bojan Jovanovic ◽

Ratko Stankovic ◽

Sasa Markovic

Keyword(s):

Evolution Equation ◽

Time Dependent ◽

Hamiltonian Form ◽

Jet Spaces ◽

Hamiltonian Equations ◽

Fibre Bundles ◽

Energetic Approach ◽

Configuration Manifold ◽

General Time

AbstractIn this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. This is the time-dependent generalization of an ‘ordinary’ autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. In our view, this time-dependent energetic approach is much more realistic than the autonomous one. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system.

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Weil bundles and jet spaces

Czechoslovak Mathematical Journal ◽

10.1023/a:1022408527395 ◽

2000 ◽

Vol 50 (4) ◽

pp. 721-748 ◽

Cited By ~ 12

Author(s):

J. Muñoz ◽

J. Rodriguez ◽

F. J. Muriel

Keyword(s):

Jet Spaces

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Cellular Legendrian contact homology for surfaces, part II

International Journal of Mathematics ◽

10.1142/s0129167x19500368 ◽

2019 ◽

Vol 30 (07) ◽

pp. 1950036

Author(s):

Daniel Rutherford ◽

Michael Sullivan

Keyword(s):

Explicit Construction ◽

Jet Spaces ◽

Contact Homology ◽

Cellular Computation ◽

Legendrian Contact Homology

This paper is a continuation of [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)]. For Legendrian surfaces in [Formula: see text]-jet spaces, we prove that the Cellular DGA defined in [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)] is stable tame isomorphic to the Legendrian contact homology DGA, modulo the explicit construction of a specific Legendrian surface. In [Cellular computation of Legendrian contact homology for surfaces, to appear in Internat. J. Math.], we construct this surface, thereby completing Theorem 5.1 and the proof of the isomorphism.

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