Finsler Geometry  

In General > s.a. Gauss-Bonnet; lie group.
* Idea: Can be locally anisotropic, and has been used to model/explain anisotropy in cosmology.
@ General references: Asanov 85; Matsumoto 86; Beil IJTP(89) [class of metrics]; Bejancu 90; Antonelli 99; Shen 01; Antonelli ed-03 [handbook]; Chern & Shen 05.
@ Related topics: Kozma et al RPMP(06) [twisted products]; Bejancu & Farran RPMP(06) [tangent bundles, positive constant curvature].

Additional Structure and Special Cases
* Randers spaces RFn: Finsler spaces Fn = (M, + ) equipped with the Cartan non-linear connection, introduced by R S Ingarden.
* Ingarden spaces IFn: Finsler spaces Fn = (M, + ) equipped with the Lorentz non-linear connection, introduced by R Miron.
@ Spinors, connections: Vacaru in(96)dg; Vargas & Torr GRG(96); Solov'yov & Vladimirov IJTP(01)mp [N-spinors]; Ikeda RPMP(05); Youssef et al a0805 [torsion and curvature of a connection].
@ Homogeneous manifolds: Deng & Hou JPA(04), JPA(06); Latifi & Razavi RPMP(06).
@ Special cases: Miron RPMP(04), RPMP(06) [Ingarden spaces]; Mo & Yang DG&A(06) [isotropic S-curvature].
@ Related topics: Józefowicz & Wolak DG&A(08) [Finslerian foliations of compact manifolds are Riemannian].

Generalizations > s.a. non-commutative geometry; Riemann-Cartan; types of fiber bundles.
@ Pseudo-Finsler structures: Skakala & Visser a0806 [and birefringent optics].
@ Finsler-Lagrange spaces: Vacaru a0707, IJGMP(08)-a0801 [rev, general relativity and string theory]; Miron RPMP(06).

And Physics > s.a. chaos in Bianchi models; doubly special relativity; modified lorentz symmetry; spacetime models.
@ General references: Bekenstein PRD(93)gq/92; Roxburgh et al Tensor(92); Golestanian et al CQG(95); Asanov mp/00 [T violation]; Stavrinos & Diakogiannis gq/02 [and anisotropy]; Asanov gq/02 [rotational symmetry violation], FPL(02)gq [and Michelson-Morley experiments], gq/02 [kinematic transformations]; Noskov G&C(04), G&C(04).
@ And spacetime structure: Beil IJTP(93) [and Kaluza-Klein theory]; Bogoslovsky & Goenner PLA(98)gq, GRG(99)gq [generalized Lorentz transformations]; Liu ht/98, CSF(01), CSF(01)ht/98, CSF(01) [modified special relativity]; Weinfurtner et al gq/06-in [analog Finsler spacetime from 2-component BEC].
@ And gravity: Ikeda AdP(90); Beil IJTP(92) [gauge transformations]; Yazaki IJMPD(94) [+ other interactions]; Panahi NCB(03)gq [Lorentzian geometry]; Huang a0710 [proposal].
@ And quantum gravity: Girelli et al PRD(07)gq/06 [modified dispersion relations].
@ And other field theory: Beil FP(03); Brandt ht/04-in [quantum field theory]; Sindoni PRD(08)-a0712 [and Higgs mechanism].
@ Geodesics: Perlick GRG(06)gq/05 [and Fermat principle]; Latifi JGP(07) [homogeneous].
@ Specific systems: Gutkin & Tabachnikov JGP(02) [billiards]; Arik & Ciftci G&C(03) [cosmological model]; De ht/03 [and hadrons]; Bogoslovsky & Goenner PLA(04)ht [and Dirac equation]; Duval a0707 [geometrical optics on Finsler manifold].

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