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ON WEAKLY-BERWALD SPACES OF SPECIAL (α, β)-METRICS

  • Published : 2006.05.01

Abstract

We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${\alpha},{\beta}$)-metrics be weakly-Berwald spaces, respectively.

Keywords

Berwald space;cubic metric space;Douglas space;Finsler space with $L={\alpha}+{\beta}^2/{\alpha}$;infinite series (${\alpha},{\beta}$)-metric space;weakly-Berwald space

References

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  1. Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric vol.18, 2017, https://doi.org/10.18052/www.scipress.com/IJPMS.18.1
  2. ON THE SECOND APPROXIMATE MATSUMOTO METRIC vol.51, pp.1, 2014, https://doi.org/10.4134/BKMS.2014.51.1.115
  3. RETRACTED: On two subclasses of -metrics being projectively related vol.62, pp.2, 2012, https://doi.org/10.1016/j.geomphys.2011.10.004