Deformational Structures on Smooth Manifolds

Details Deformational Structures on Smooth Manifolds Deformational Structures on Smooth Manifolds

2002-11-02

arxiv.org/abs/math-ph/0211004v1

Trends of Mathematical Physics (2004), pp. 113-154, ed. by C.V.Benton, Nova Science Publisher, New York

Physics

Mathematical Physics

This is developed variant of talk, given at the 5-th ICGA conference (Russia,Moscow, October 2001). To be published in Acta Ph

Scientific paper

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decomposition of manifolds, generalizing isometry of Riemannian spaces and consider some physical examples. In frame of dynamical deformational structures we formulate variational procedure for evolutional and static cases together with boundary conditions, derive dynamical (equilibrium in static case) equations, consider perturbative approach and perform deformational realization of the well known classical field-theoretical topics: strings and branes theories, classical mechanics of solids, gravity and Maxwell electrodynamics.

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