Conformal vector fields on Finsler manifolds

József Szilasi; Anna Tóth

Communications in Mathematics (2011)

  • Volume: 19, Issue: 2, page 149-168
  • ISSN: 1804-1388

Abstract

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Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.

How to cite

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Szilasi, József, and Tóth, Anna. "Conformal vector fields on Finsler manifolds." Communications in Mathematics 19.2 (2011): 149-168. <http://eudml.org/doc/246872>.

@article{Szilasi2011,
abstract = {Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.},
author = {Szilasi, József, Tóth, Anna},
journal = {Communications in Mathematics},
keywords = {spray manifold; Finsler manifold; projective vector field; affine vector field; conformal vector field; conformal vector field; Finsler manifold},
language = {eng},
number = {2},
pages = {149-168},
publisher = {University of Ostrava},
title = {Conformal vector fields on Finsler manifolds},
url = {http://eudml.org/doc/246872},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Szilasi, József
AU - Tóth, Anna
TI - Conformal vector fields on Finsler manifolds
JO - Communications in Mathematics
PY - 2011
PB - University of Ostrava
VL - 19
IS - 2
SP - 149
EP - 168
AB - Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection (‘pull-back formalism’), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.
LA - eng
KW - spray manifold; Finsler manifold; projective vector field; affine vector field; conformal vector field; conformal vector field; Finsler manifold
UR - http://eudml.org/doc/246872
ER -

References

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  1. Abraham, R., Marsden, J.E., Ratiu, T., Manifolds, Tensor Analysis, and Applications, 2nd edition, Springer-Verlag, New York and Berlin 1988 (1988) Zbl0875.58002MR0960687
  2. Akbar-Zadeh, H., Transformations infinitésimales conformes des variétés finsleriennes compactes, Annales Polonici Mathematici XXXVI 1979 213-229 (1979) Zbl0413.53036MR0537616
  3. Akbar-Zadeh, H., Champs de vecteurs projectifs sur le fibré unitaire, J. Math. pures et appl. 65 1986 47-79 (1986) MR0844240
  4. Bácsó, S., Szilasi, Z., On the projective theory of sprays, Acta Math. Acad. Paed. Nyregyháziensis 26 2010 171-207 (2010) Zbl1240.53047MR2754415
  5. Crampin, M., 10.1112/jlms/s2-3.1.178, J. London Math. Soc (2) 3 1971 178-182 (1971) Zbl0215.51003MR0293528DOI10.1112/jlms/s2-3.1.178
  6. León, M. de, Rodrigues, P.R., Methods of Differential Geometry in Analytical Mechanics, North-Holland, Amsterdam 1989 (1989) Zbl0687.53001MR1021489
  7. Greub, W., Halperin, S., Vanstone, R., Connections, Curvature, and Cohomology, Vol. I, Academic Press, New York and London 1972 (1972) Zbl0322.58001
  8. Grifone, J., 10.5802/aif.407, Ann. Inst. Fourier (Grenoble) 22 1972 287-334 (1972) Zbl0219.53032MR0336636DOI10.5802/aif.407
  9. Grifone, J., Transformations infinitésimales conformes d’une variété finslerienne, C.R. Acad. Sc. Paris 280, Série A 1975 519-522 (1975) Zbl0311.53071MR0388300
  10. Grifone, J., Sur les transformations infinitésimales conformes d’une variété finslérienne, C.R. Acad. Sc. Paris 280, Série A 1975 583-585 (1975) Zbl0311.53071MR0370450
  11. Lang, S., Fundamentals of Differential Geometry, Springer-Verlag, New York 1999 (1999) Zbl0932.53001MR1666820
  12. Lovas, R.L., 10.1023/B:MAHU.0000038973.18653.2e, Periodica Mathematica Hungarica 48 2004 165-179 (2004) Zbl1067.53059MR2077694DOI10.1023/B:MAHU.0000038973.18653.2e
  13. Matsumoto, M., Theory of extended point transformations of Finsler spaces I, Tensor N.S. 45 1987 109-115 (1987) Zbl0637.53031
  14. Matsumoto, M., Theory of extended point transformations of Finsler spaces II, Tensor N.S. 47 1988 203-214 (1988) Zbl0701.53046MR1037236
  15. Misra, R.B., Groups of transformations in Finslerian spaces, Internal Reports of the ICTP, Trieste 1993 (1993) 
  16. Szilasi, J., A Setting for Spray and Finsler Geometry, Handbook of Finsler Geometry , Kluwer Academic Publishers, Dordrecht 2003 1183-1426 (2003) Zbl1105.53043MR2066454
  17. Szilasi, J., Vincze, Cs., On conformal equivalence of Riemann-Finsler metrics, Publ. Math. Debrecen 52 1998 167-185 (1998) Zbl0907.53044MR1603351
  18. Yano, K., The Theory of Lie Derivatives and its Applications, North-Holland, Amsterdam 1957 (1957) Zbl0077.15802MR0088769
  19. Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc., New York 1973 (1973) Zbl0262.53024MR0350650

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