| Title:
|
Homogeneous variational problems and Lagrangian sections (English) |
| Author:
|
Saunders, D.J. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
24 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
115-123 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define a canonical line bundle over the slit tangent bundle of a manifold, and define a Lagrangian section to be a homogeneous section of this line bundle. When a regularity condition is satisfied the Lagrangian section gives rise to local Finsler functions. For each such section we demonstrate how to construct a canonically parametrized family of geodesics, such that the geodesics of the local Finsler functions are reparametrizations. (English) |
| Keyword:
|
Finsler geometry |
| Keyword:
|
line bundle |
| Keyword:
|
geodesics |
| MSC:
|
53C22 |
| MSC:
|
53C60 |
| idZBL:
|
Zbl 1360.53077 |
| idMR:
|
MR3590209 |
| . |
| Date available:
|
2017-02-28T16:41:21Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146015 |
| . |
| Reference:
|
[1] Chern, S.-S.: Finsler geometry is just Riemannian geometry without the quadratic restriction.Not. A.M.S., 43, 9, 1996, 959-963, Zbl 1044.53512, MR 1400859 |
| Reference:
|
[2] Crampin, M.: Some remarks on the Finslerian version of Hilbert's Fourth Problem.Houston J. Math., 37, 2, 2011, 369-391, Zbl 1228.53085, MR 2794554 |
| Reference:
|
[3] Crampin, M., Mestdag, T., Saunders, D.J.: The multiplier approach to the projective Finsler metrizability problem.Diff. Geom. Appl., 30, 6, 2012, 604-621, Zbl 1257.53105, MR 2996856, 10.1016/j.difgeo.2012.07.004 |
| Reference:
|
[4] Crampin, M., Saunders, D.J.: Projective connections.J. Geom. Phys., 57, 2, 2007, 691-727, Zbl 1114.53014, MR 2271212, 10.1016/j.geomphys.2006.03.007 |
| Reference:
|
[5] Hebda, J., Roberts, C.: Examples of Thomas--Whitehead projective connections.Diff. Geom. Appl., 8, 1998, 87-104, Zbl 0897.53009, MR 1601526 |
| Reference:
|
[6] Massa, E., Pagani, E., Lorenzoni, P.: On the gauge structure of classical mechanics.Transport Theory and Statistical Physics, 29, 1--2, 2000, 69-91, Zbl 0968.70014, MR 1774182, 10.1080/00411450008205861 |
| Reference:
|
[7] Roberts, C.: The projective connections of T.Y. Thomas and J.H.C. Whitehead applied to invariant connections.Diff. Geom. Appl., 5, 1995, 237-255, Zbl 0833.53023, MR 1353058, 10.1016/0926-2245(95)92848-Y |
| Reference:
|
[8] Thomas, T.Y.: A projective theory of affinely connected manifolds.Math. Zeit., 25, 1926, 723-733, MR 1544836, 10.1007/BF01283864 |
| . |
