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Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications

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Abstract

We present a generalization of the spinor and twistor geometry for (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler–Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors are defined as solutions of generalized twistor equations determined by spin connections and frames adapted to nonlinear connection structures. We show that the constructions for local twistors can be globalized using nonholonomic deformations with “auxiliary” metric compatible connections completely determined by the metric structure and/or the Finsler fundamental function. We explain how to perform such an approach in the Einstein gravity theory formulated in Finsler like variables with conventional nonholonomic 2+2 splitting.

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Authors and Affiliations

  1. Associated visiting research affiliation: Theory Division, CERN, 1211, Geneva 23, Switzerland

    Sergiu I. Vacaru

  2. Rector’s Office, Alexandru Ioan Cuza University, Alexandru Lapuşneanu Street 14, UAIC – Corpus R, office 323, Iaşi, 700057, Romania

    Sergiu I. Vacaru

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Vacaru, S.I. Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications. Adv. Appl. Clifford Algebras 25, 453–485 (2015). https://doi.org/10.1007/s00006-014-0513-x

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