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 Sergiu I. Vacaru and Nadejda A. Vicol. 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.