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- W1754817895 abstract "We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic man- ifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann- Cartan space) defined by a generic off-diagonal metric structure (with an additional affine connection possessing nontrivial torsion) is equiv- alent to a generalized Lagrange, or Finsler, geometry modeled on non- holonomic manifolds. This results in the problem of constructing non- commutative geometries with local anisotropy, in particular, related to geometrization of classical and quantum mechanical and field theories, even if we restrict our considerations only to commutative and non- commutative Riemannian spaces. We elaborate a geometric approach to the Clifford modules adapted to nonlinear connections, to the the- ory of spinors and the Dirac operators on nonholonomic spaces and consider possible generalizations to noncommutative geometry. We argue that any commutative Riemann-Finsler geometry and general- izations my be derived from noncommutative geometry by applying" @default.
- W1754817895 created "2016-06-24" @default.
- W1754817895 creator A5015978782 @default.
- W1754817895 date "2004-08-09" @default.
- W1754817895 modified "2023-09-27" @default.
- W1754817895 title "Nonholonomic Clifford Structures and Noncommutative Riemann-Finsler Geometry" @default.
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