Acknowledgement
Supported by : National Natural Science Foundation of China, Youth Science Fund of Henan Normal University, doctoral scientific research foundation of Henan Normal University
References
- 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.
- D. Bao, C. Robles, and Z. Shen, Zermelo navigation on Riemannian manifolds, J. Differential Geom. 66 (2004), no. 3, 377-435. https://doi.org/10.4310/jdg/1098137838
- R. Bryant, Some remarks on Finsler manifolds with constant flag curvature, Houston J. Math. 28 (2002), no. 2, 221-262.
- X. Chen, X. Mo, and Z. Shen, On the flag curvature of Finsler metrics of scalar curvature, J. London Math. Soc. 68 (2003), no. 3, 762-780. https://doi.org/10.1112/S0024610703004599
- X. Chen and Z. Shen, Randers metrics with special curvature properties, Osaka J. Math. 40 (2003), no. 1, 87-101.
- X. Chen and Z. Shen, On Douglas metrics, Publ. Math. Debreen 66 (2007), 503-512.
- X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J. Math. 169 (2009), 317-340. https://doi.org/10.1007/s11856-009-0013-1
-
X. Cheng, Z. Shen, and Y. Tian, Einstein (
${\alpha},\;{\beta}$ )-metrics, Israel J. Math. 192 (2012), no. 1, 221-249. https://doi.org/10.1007/s11856-012-0036-x - S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics, 25 Vol. 6 (World Scientific Publishing, Hackensack, NJ, 2005), x+192 pp.
- E. Guo, H. Liu, and X. Mo, On spherically symmetric Finsler metrics with isotropic Berwald curvature, Int. J. Geom. Methods Mod. Phys. 10 (2013), no. 10, 1350054, 13 pp. https://doi.org/10.1142/S0219887813500540
- B. Li and Z. Shen, Projectively flat fourth root Finsler metrics, Can. Math. Bull. 55 (2012), no. 1, 138-145. https://doi.org/10.4153/CMB-2011-056-5
- X. Mo and H. Zhu, On a class of projectively flat Finsler metrics of negative constant flag curvature, Internat. J. Math. 23 (2012), no. 8, 1250084, 14 pp. https://doi.org/10.1142/S0129167X1250084X
- Z. Shen, Diffierential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.
- Z. Shen and C. Yu, On a class of Einstein Finsler metrics, Internat. J. Math. 25 (2014), no. 4, 1450030, 18 pp. https://doi.org/10.1142/S0129167X1450030X
- A. Tayebi and B. Najafi, On isotropic Berwald metric, Ann. Polon. Math. 103 (2012), no. 2, 109-121. https://doi.org/10.4064/ap103-2-1
- A. Tayebi and M. Rafie-Rad, S-curvature of isotropic Berwald metrics, Sci. China Ser. A 51 (2008), no. 12, 2198-2204. https://doi.org/10.1007/s11425-008-0095-y
- C. Yu and H. Zhu, On a new class of Finsler metrics, Differential Geom. Appl. 29 (2011), no. 2, 244-254. https://doi.org/10.1016/j.difgeo.2010.12.009
-
C. Yu and H. Zhu, Projectively flat general (
${\alpha},\;{\beta}$ )-metrics with constant flag curvature, J. Math. Anal. Appl. 429 (2015), no. 2, 1222-1239. https://doi.org/10.1016/j.jmaa.2015.04.072 - H. Zhu, A class of Finsler metrics of scalar flag curvature, Differntial Geom. Appl. 40 (2015), 321-331. https://doi.org/10.1016/j.difgeo.2015.02.011
-
H. Zhu, On general (
${\alpha},\;{\beta}$ )-metrics with vanishing Douglas curvature, Internat. J. Math. 26 (2015), no. 9, 1550076, 16 pp. https://doi.org/10.1142/S0129167X15500767
Cited by
- On a class of almost regular Landsberg metrics pp.1869-1862, 2019, https://doi.org/10.1007/s11425-017-9290-6