Finsler
Geometry| 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;
Tamássy DG&A(08) [relationship with metric spaces].
@ Related topics: Kozma et al RPMP(06)
[twisted products]; Bejancu & Farran RPMP(06)
[tangent bundles, positive constant
curvature]; Mo DG&A(09) [non-Riemannian invariant H].
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,
a0810-in
[and
birefringent
optics].
@ Finsler-Lagrange spaces: Vacaru a0707,
IJGMP(08)-a0801,
SIGMA(08)-a0806 [rev,
general relativity and string theory];
Miron RPMP(06).
And Physics > s.a. chaos
in Bianchi models; doubly special relativity;
modified lorentz symmetry; path
integrals; Very Special Relativity.
* Motivation: A
Finsler structure is one possible way to model a small-scale breaking of
Lorentz invariance.
@ 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);
Lämmerzahl et al GRG(09)-a0811 [and
experiment].
@ 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 LNP(07)gq/06 [analog
Finsler spacetime from 2-component BEC]; Caponio et al a0903 [and
Lorentzian
causality]; Tavakol IJMPA(09)
[rev]; Gallego a0906 [semi-Randers
space as spacetime structure]; > s.a. history
of relativity, spacetime
models.
@ Gravity:
Ikeda AdP(90);
Beil IJTP(92)
[gauge transformations]; Yazaki IJMPD(94)
[+ other interactions]; Panahi NCB(03)gq [Lorentzian
geometry]; Huang a0710 [proposal].
@ Quantum gravity: Girelli et al PRD(07)gq/06 [modified
dispersion relations].
@ Spinors: Bogoslovsky & Goenner PLA(04)ht [Dirac
equation]; Solov'yov
a0906 [Finslerian 3-spinors].
@ Other field theory:
Beil FP(03);
Brandt ht/04-in
[quantum field theory]; Sindoni PRD(08)-a0712 [and
Higgs mechanism]; Voicu-Brinzei & Siprov a0905 {electromagnetism].
@ 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]; Duval CMP(08)-a0707 [geometrical
optics on Finsler manifold].
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send feedback and suggestions to bombelli at olemiss.edu – modified 17
jun
2009