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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 23, Pages 1189-1237

Nonlinear connections and spinor geometry

1Centro Multidisciplinar de Astrofisica - CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Lisboa 1049-001, Portugal
2Faculty of Mathematics and Informatics, State University of Moldova, Chişinău MD 2009, Moldova

Received 21 December 2002

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an introduction to the geometry of higher-order vector and covector bundles (including higher-order generalizations of the Finsler geometry and Kaluza-Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for application of Finsler-like geometries in modern string and gravity theory, noncommutative geometry and noncommutative field theory, and gravity.