Conformal vector fields on Finsler manifolds. (English) Zbl 1247.53089

Using notions and techniques from classical tangent bundle geometry and using tools from the calculus along tangent bundle projection the present work gives new characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Several interesting properties of these classes of vector fields are obtained.
Reviewer: Radu Miron (Iaşi)


53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53A30 Conformal differential geometry (MSC2010)
Full Text: arXiv EuDML


[1] Abraham, R., Marsden, J.E., Ratiu, T.: Manifolds, Tensor Analysis, and Applications. 2nd edition, Springer-Verlag, New York and Berlin 1988 · Zbl 0875.58002
[2] Akbar-Zadeh, H.: Transformations infinitésimales conformes des variétés finsleriennes compactes. Annales Polonici Mathematici XXXVI 1979 213-229 · Zbl 0413.53036
[3] Akbar-Zadeh, H.: Champs de vecteurs projectifs sur le fibré unitaire. J. Math. pures et appl. 65 1986 47-79 · Zbl 0582.53027
[4] Bácsó, S., Szilasi, Z.: On the projective theory of sprays. Acta Math. Acad. Paed. Nyregyháziensis 26 2010 171-207 · Zbl 1240.53047
[5] Crampin, M.: On horizontal distributions on the tangent bundle of a differentiable manifold. J. London Math. Soc (2) 3 1971 178-182 · Zbl 0215.51003
[6] León, M. de, Rodrigues, P.R.: Methods of Differential Geometry in Analytical Mechanics. North-Holland, Amsterdam 1989 · Zbl 0687.53001
[7] Greub, W., Halperin, S., Vanstone, R.: Connections, Curvature, and Cohomology. Vol. I, Academic Press, New York and London 1972 · Zbl 0322.58001
[8] Grifone, J.: Structure presque-tangente et connexions, I. Ann. Inst. Fourier (Grenoble) 22 1972 287-334 · Zbl 0219.53032
[9] Grifone, J.: Transformations infinitésimales conformes d’une variété finslerienne. C.R. Acad. Sc. Paris 280, Série A 1975 519-522 · Zbl 0311.53071
[10] Grifone, J.: Sur les transformations infinitésimales conformes d’une variété finslérienne. C.R. Acad. Sc. Paris 280, Série A 1975 583-585 · Zbl 0311.53071
[11] Lang, S.: Fundamentals of Differential Geometry. Springer-Verlag, New York 1999 · Zbl 0932.53001
[12] Lovas, R.L.: Affine and projective vector fields on spray manifolds. Periodica Mathematica Hungarica 48 2004 165-179 · Zbl 1067.53059
[13] Matsumoto, M.: Theory of extended point transformations of Finsler spaces I. Tensor N.S. 45 1987 109-115 · Zbl 0637.53031
[14] Matsumoto, M.: Theory of extended point transformations of Finsler spaces II. Tensor N.S. 47 1988 203-214 · Zbl 0701.53046
[15] Misra, R.B.: Groups of transformations in Finslerian spaces. Internal Reports of the ICTP, Trieste 1993
[16] Szilasi, J.: A Setting for Spray and Finsler Geometry. Handbook of Finsler Geometry , Kluwer Academic Publishers, Dordrecht 2003 1183-1426 · Zbl 1105.53043
[17] Szilasi, J., Vincze, Cs.: On conformal equivalence of Riemann-Finsler metrics. Publ. Math. Debrecen 52 1998 167-185 · Zbl 0907.53044
[18] Yano, K.: The Theory of Lie Derivatives and its Applications. North-Holland, Amsterdam 1957 · Zbl 0077.15802
[19] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles. Marcel Dekker Inc., New York 1973 · Zbl 0262.53024
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