| Title:
|
Projective metrizability in Finsler geometry (English) |
| Author:
|
Saunders, David |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
20 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
63-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. This paper describes an approach to the problem using an analogue of the multiplier approach to the inverse problem in Lagrangian mechanics. (English) |
| Keyword:
|
Finsler function |
| Keyword:
|
spray |
| Keyword:
|
projective equivalence |
| Keyword:
|
geodesic path |
| Keyword:
|
projective metrizability |
| Keyword:
|
Hilbert form |
| MSC:
|
53C60 |
| idZBL:
|
Zbl 06202719 |
| idMR:
|
MR3001632 |
| . |
| Date available:
|
2012-11-27T16:31:13Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143081 |
| . |
| Reference:
|
[1] Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler Geometry.2000, Springer Zbl 0954.53001, MR 1747675 |
| Reference:
|
[2] 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:
|
[3] Crampin, M., Mestdag, T., Saunders, D.J.: Hilbert forms for a Finsler metrizable projective class of sprays.Diff. Geom. Appl., to appear |
| Reference:
|
[4] Krupková, O., Prince, G.E.: Second order ordinary differential equations in jet bundles and the inverse problem of the calculus of variations.Handbook of Global Analysis, 2008, 837-904, Elsevier Zbl 1236.58027, MR 2389647 |
| Reference:
|
[5] Shen, Z.: Differential Geometry of Spray and Finsler Spaces.2001, Kluwer Zbl 1009.53004, MR 1967666 |
| Reference:
|
[6] Whitehead, J.H.C.: Convex regions in the geometry of paths.Quart. J. Math., 3, 1932, 33-42 Zbl 0004.13102, 10.1093/qmath/os-3.1.33 |
| Reference:
|
[7] Whitehead, J.H.C.: Convex regions in the geometry of paths -- addendum.Quart. J. Math., 4, 1933, 226-227 Zbl 0007.36801, 10.1093/qmath/os-4.1.226 |
| . |
