Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 008, 9 pages      arXiv:1001.3654      http://dx.doi.org/10.3842/SIGMA.2010.008

On Special Berwald Metrics

Akbar Tayebi a and Esmaeil Peyghan b
a) Department of Mathematics, Faculty of Science, Qom University, Qom, Iran
b) Department of Mathematics, Faculty of Science, Arak University, Arak, Iran

Received November 01, 2009, in final form January 17, 2010; Published online January 20, 2010

Abstract
In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature Finsler metrics in this class. Finally we show that on this class of Finsler metrics, the notion of Landsberg and weakly Landsberg curvature are equivalent.

Key words: Randers metric; Douglas curvature; Berwald curvature.

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References

  1. Akbar-Zadeh H., Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci. (5) 74 (1988), no. 10, 271-322.
  2. Antonelli P.L., Handbook of Finsler geometry, Kluwer Academic Publishers, Dordrecht, 2003.
  3. Berwald L., Über Parallelübertragung in Räumen mit allgemeiner Massbestimmung, Jahresbericht D.M.V. 34 (1926), 213-220.
  4. Bácsó S., Matsumoto M., On Finsler spaces of Douglas type - a generalization of notion of Berwald space, Publ. Math. Debrecen 51 (1997), 385-406.
  5. Bácsó S., Papp I., A note on a generalized Douglas space, Period. Math. Hungar. 48 (2004), 181-184.
  6. Chen X., Shen Z., On Douglas metrics, Publ. Math. Debrecen 66 (2005), 503-512.
  7. Ichijyo Y., Finsler manifolds modeled on a Minkowski space, J. Math. Kyoto Univ. 16 (1976), 639-652.
  8. Matsumoto M., On C-reducible Finsler spaces, Tensor (N.S.) 24 (1972), 29-37.
  9. Matsumoto M., Hojo S., A conclusive theorem for C-reducible Finsler spaces, Tensor (N.S.) 32 (1978), 225-230.
  10. Najafi B., Shen Z., Tayebi A., On a projective class of Finsler metrics, Publ. Math. Debrecen 70 (2007), 211-219.
  11. Najafi B., Shen Z., Tayebi A., Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata 131 (2008), 87-97.
  12. Pande H.D., Tripathi P.N., Prasad B.N., On a special form of the hv-curvature tensor of Berwald's connection BΓ of Finsler space, Indian J. Pure. Appl. Math. 25 (1994), 1275-1280.
  13. Shen Z., Lectures on Finsler geometry, World Scientific Publishing Co., Singapore, 2001.
  14. Shen Z., Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001.
  15. Tayebi A., Azizpour E., Esrafilian E., On a family of connections in Finsler geometry, Publ. Math. Debrecen 72 (2008), 1-15.
  16. Tayebi A., Rafie Rad M., S-curvature of isotropic Berwald metrics, Sci. China Ser. A 51 (2008), 2198-2204.

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