Projective metrizability in Finsler geometry

David Saunders

Communications in Mathematics (2012)

  • Volume: 20, Issue: 1, page 63-68
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Saunders, David. "Projective metrizability in Finsler geometry." Communications in Mathematics 20.1 (2012): 63-68. <http://eudml.org/doc/246622>.

@article{Saunders2012,
abstract = {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.},
author = {Saunders, David},
journal = {Communications in Mathematics},
keywords = {Finsler function; spray; projective equivalence; geodesic path; projective metrizability; Hilbert form; Finsler function; spray; projective equivalence; geodesic path; projective metrizability; Hilbert form},
language = {eng},
number = {1},
pages = {63-68},
publisher = {University of Ostrava},
title = {Projective metrizability in Finsler geometry},
url = {http://eudml.org/doc/246622},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Saunders, David
TI - Projective metrizability in Finsler geometry
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 1
SP - 63
EP - 68
AB - 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.
LA - eng
KW - Finsler function; spray; projective equivalence; geodesic path; projective metrizability; Hilbert form; Finsler function; spray; projective equivalence; geodesic path; projective metrizability; Hilbert form
UR - http://eudml.org/doc/246622
ER -

References

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  1. Bao, D., Chern, S.-S., Shen, Z., An Introduction to Riemann-Finsler Geometry, 2000, Springer (2000) Zbl0954.53001MR1747675
  2. Crampin, M., Mestdag, T., Saunders, D.J., 10.1016/j.difgeo.2012.07.004, Diff. Geom. Appl., 30, 6, 2012, 604-621 (2012) Zbl1257.53105MR2996856DOI10.1016/j.difgeo.2012.07.004
  3. Crampin, M., Mestdag, T., Saunders, D.J., Hilbert forms for a Finsler metrizable projective class of sprays, Diff. Geom. Appl., to appear 
  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 (2008) Zbl1236.58027MR2389647
  5. Shen, Z., Differential Geometry of Spray and Finsler Spaces, 2001, Kluwer (2001) Zbl1009.53004MR1967666
  6. Whitehead, J.H.C., 10.1093/qmath/os-3.1.33, Quart. J. Math., 3, 1932, 33-42 (1932) Zbl0004.13102DOI10.1093/qmath/os-3.1.33
  7. Whitehead, J.H.C., 10.1093/qmath/os-4.1.226, Quart. J. Math., 4, 1933, 226-227 (1933) Zbl0007.36801DOI10.1093/qmath/os-4.1.226

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