FINSLER AND LAGRANGE GEOMETRIES IN EINSTEIN AND STRING GRAVITY
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- 1 June 2008
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Geometric Methods in Modern Physics
- Vol. 5 (4), 473-511
- https://doi.org/10.1142/s0219887808002898
Abstract
We review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler geometry and geometric mechanics how they could perform their results in order to be accepted by the community of "orthodox" physicists. Although the bulk of former models of Finsler–Lagrange spaces where elaborated on tangent bundles, the surprising result advocated in our works is that such locally anisotropic structures can be modeled equivalently on Riemann–Cartan spaces, even as exact solutions in Einstein and/or string gravity, if nonholonomic distributions and moving frames of references are introduced into consideration. We also propose a canonical scheme when geometrical objects on a (pseudo) Riemannian space are nonholonomically deformed into generalized Lagrange, or Finsler, configurations on the same manifold. Such canonical transforms are defined by the coefficients of a prime metric and generate target spaces as Lagrange structures, their models of almost Hermitian/Kähler, or nonholonomic Riemann spaces. Finally, we consider some classes of exact solutions in string and Einstein gravity modeling Lagrange–Finsler structures with solitonic pp-waves and speculate on their physical meaning.Keywords
This publication has 40 references indexed in Scilit:
- Clifford-Finsler algebroids and nonholonomic Einstein–Dirac structuresJournal of Mathematical Physics, 2006
- Exact solutions with noncommutative symmetries in Einstein and gauge gravityJournal of Mathematical Physics, 2005
- Lagrange–Fedosov nonholonomic manifoldsJournal of Mathematical Physics, 2005
- Higher-order mechanical systems with constraintsJournal of Mathematical Physics, 2000
- A Kaehler structure on the nonzero tangent bundle of a space formDifferential Geometry and its Applications, 1999
- Yang-mills fields and gauge gravity on generalized Lagrange and Finsler spacesInternational Journal of Theoretical Physics, 1995
- Relation between physical and gravitational geometryPhysical Review D, 1993
- Lagrange geometryArchiv der Mathematik, 1974
- Some Gravitational WavesPhysical Review Letters, 1959
- Untersuchung der Krümmung allgemeiner metrischer Räume auf Grund des in ihnen herrschenden ParallelismusMathematische Zeitschrift, 1926