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

Title & Authors
ON WEAKLY-BERWALD SPACES OF SPECIAL (α, β)-METRICS
Lee, Il-Yong; Lee, Myung-Han;

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 ($\small{{\alpha},{\beta}}$)-metric be a weakly-Berwald space and the Finsler spaces with some special ($\small{{\alpha},{\beta}}$)-metrics be weakly-Berwald spaces, respectively.
Keywords
Berwald space;cubic metric space;Douglas space;Finsler space with $L Language English Cited by 1. ON THE SECOND APPROXIMATE MATSUMOTO METRIC,;;; 대한수학회보, 2014. vol.51. 1, pp.115-128 1. Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric, International Journal of Pure Mathematical Sciences, 2017, 18, 1 2. ON THE SECOND APPROXIMATE MATSUMOTO METRIC, Bulletin of the Korean Mathematical Society, 2014, 51, 1, 115 3. RETRACTED: On two subclasses of -metrics being projectively related, Journal of Geometry and Physics, 2012, 62, 2, 292 References 1. S. Bacso and M. Matsumoto, On Finsler spaces of Douglas type. A generalization of the notion of Berwald space, Publ. Math. Debrecen 51 (1997), no. 3-4, 385-406 2. S. Bacso and B. Szilagyi, On a weakly Berwald Finsler space of Kropina type, Math. Pannon. 13 (2002), no. 1, 91-95 3. S. Bacso and R. Yoshikawa, Weakly-Berwald spaces, Publ. Math. Debrecen 61 (2002), no. 2, 219-231 4. M. Hashiguchi, S. Hojo, and M. Matsumoto, Landsberg spaces of dimension two with ($\alpha,\;\beta$)-metric, Tensor (N. S.) 57 (1996), no. 2, 145-153 5. M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Otsu, Saikawa (1986) 6. M. Matsumoto, The Berwald connection of a Finsler space with an ($\alpha,\;\beta$)-metric, Tensor (N. S.) 50 (1991), no. 1, 18-21 7. M. Matsumoto, Theory of Finsler spaces with ($\alpha,\;\beta$)-metric, Rep. Math. Phys. 31 (1992), 43-83 8. M. Matsumoto, Finsler spaces with ($\alpha,\;\beta$)-metric of Douglas type, Tensor (N. S.) 60 (1998), no. 2, 123-134 9. M. Matsumoto and S. Numata, On Finsler space with a cubic metric, Tensor (N. S.) 33 (1979), no. 2, 153-162 10. I. Y. Lee and H. S. Park, Finsler spaces with infinite series ($\alpha,\;\beta$)-metric, J. Korean Math. Soc. 41 (2004), no. 3, 567-589 11. I. Y. Lee and D. G. Jun, On two-dimensional Landsberg space of a cubic Finsler space, East Asian Math. J. 19 (2003), no. 2, 305-316 12. R. Yoshikawa and K. Okubo, The conditions for some ($\alpha,\;\beta\$)-metric spaces to be weakly-Berwald spaces, Proceedings of the 38-th Symposium on Finsler geometry, Nov. 12-15, (2003), 54-57