International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 21-24, Pages 1189-1237
doi:10.1155/S0161171204212170
Nonlinear connections and spinor geometry
Sergiu I. Vacaru1
and Nadejda A. Vicol2
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
Abstract
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.