By Benz W.

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The unification scheme in the framework of string/ brane theory indicates that the classical (pseudo) Riemannian description is not valid on all scales of interactions. It turns out that low–energy dilaton and axi–dilaton interactions are tractable in terms of non–Riemannian mathematical structures possessing in particular anholonomic (super) frame [equivalently, (super) vielbein] fields [6], noncommutative geometry [7], quantum group structures [8] all containing, in general, nontrivial torsion and nonmetricity fields.

We refer also to applications of Finsler geometry in the theory of stochastic processes and kinetics and thermodynamics in curved spaces [61, 63]. Perhaps, the original idea on Finsler structures on phase spaces came from the A. A. Vlasov monograph [91]. The locally anisotropic processes in the language of Finsler geometry and generalizations were investigated in parallel by S. Vacaru [50, 51, 52, 55, 61, 60] and by P. Antonelli, T. Zastavniak and D. Hrimiuc (see details and a number of applications in Refs.

Phys. 37 (1996) 508–524 [55] S. Vacaru, Locally Anisotropic Stochastic Processes in Fiber Bundles, Proceeding of the Workshop ”Global Analysis, Differential Geometry and Lie Algebras”, December 16-18, 1995, Thessaloniki, Greece, ed. G. Tsagas (Geometry Balkan Press, Bucharest, 1997) 123140; gr–qc/ 9604014 [56] S. Vacaru, Locally Anisotropic Gravity and Strings, Ann. Phys. (NY), 256 (1997) 39-61 [57] S. Vacaru, Superstrings in Higher Order Extensions of Finsler Superspaces, Nucl. Phys. B, 434 (1997) 590 BIBLIOGRAPHY xlvii [58] S.

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A Beckman Quarles Type Theorem for Plane Lorentz Transformations by Benz W.


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