Homogeneous Finsler spaces and the flag-wise positively curved condition

References

[1] S. Bácsó, X. Cheng and Z. Shen, Curvature properties of (α,β)-metrics, Finsler Geometry (Sapporo 2005), Adv. Stud. Pure Math. 48, Mathematical Society of Japan, Tokyo (2007), 73–110. 10.2969/aspm/04810073Search in Google Scholar

[2] D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann–Finsler Geometry, Grad. Texts in Math. 200, Springer, New York, 2000. 10.1007/978-1-4612-1268-3Search in Google Scholar

[3] D. Bao, C. Robles and Z. Shen, Zermelo navigation on Riemannian manifolds, J. Differential Geom. 66 (2004), no. 3, 377–435. 10.4310/jdg/1098137838Search in Google Scholar

[4] L. Berard-Bergery, Les variétés riemanniennes homogènes simplement connexes de dimension impaire à courbure strictement positive, J. Math. Pures Appl. (9) 55 (1976), no. 1, 47–67. Search in Google Scholar

[5] S.-S. Chern and Z. Shen, Riemann–Finsler Geometry, Nankai Tracts Math. 6, World Scientific, Hackensack, 2005. 10.1142/5263Search in Google Scholar

[6] S. Deng and Z. Hou, Invariant Finsler metrics on homogeneous manifolds, J. Phys. A 37 (2004), no. 34, 8245–8253. 10.1088/0305-4470/37/34/004Search in Google Scholar

[7] S. Deng and Z. Hu, Curvatures of homogeneous Randers spaces, Adv. Math. 240 (2013), 194–226. 10.1016/j.aim.2013.02.002Search in Google Scholar

[8] Z. Hu and S. Deng, Homogeneous Randers spaces with isotropic S-curvature and positive flag curvature, Math. Z. 270 (2012), no. 3–4, 989–1009. 10.1007/s00209-010-0836-9Search in Google Scholar

[9] L. Huang, On the fundamental equations of homogeneous Finsler spaces, Differential Geom. Appl. 40 (2015), 187–208. 10.1016/j.difgeo.2014.12.009Search in Google Scholar

[10] L. Huang and X. Mo, On the flag curvature of a class of Finsler metrics produced by the navigation problem, Pacific J. Math. 277 (2015), no. 1, 149–168. 10.2140/pjm.2015.277.149Search in Google Scholar

[11] X. Mo and L. Hang, On curvature decreasing property of a class of navigation problems, Publ. Math. Debrecen 71 (2007), no. 1–2, 141–163. 10.5486/PMD.2007.3672Search in Google Scholar

[12] G. Randers, On an asymmetrical metric in the fourspace of general relativity, Phys. Rev. (2) 59 (1941), 195–199. 10.1103/PhysRev.59.195Search in Google Scholar

[13] M. Xu, Examples of flag-wise positively curved spaces, Differential Geom. Appl. 52 (2017), 42–50. 10.1016/j.difgeo.2017.03.015Search in Google Scholar

[14] M. Xu and S. Deng, Homogeneous (α,β)-spaces with positive flag curvature and vanishing S-curvature, Nonlinear Anal. 127 (2015), 45–54. 10.1016/j.na.2015.06.028Search in Google Scholar

[15] M. Xu and S. Deng, Normal homogeneous Finsler spaces, Transform. Groups 22 (2017), no. 4, 1143–1183. 10.1007/s00031-017-9428-7Search in Google Scholar

[16] M. Xu and S. Deng, Towards the classification of odd-dimensional homogeneous reversible Finsler spaces with positive flag curvature, Ann. Mat. Pura Appl. (4) 196 (2017), no. 4, 1459–1488. 10.1007/s10231-016-0624-1Search in Google Scholar

[17] M. Xu, S. Deng, L. Huang and Z. Hu, Even-dimensional homogeneous Finsler spaces with positive flag curvature, Indiana Univ. Math. J. 66 (2017), no. 3, 949–972. 10.1512/iumj.2017.66.6040Search in Google Scholar

[18] M. Xu and J. A. Wolf, Killing vector fields of constant length on Riemannian normal homogeneous spaces, Transform. Groups 21 (2016), no. 3, 871–902. 10.1007/s00031-016-9380-ySearch in Google Scholar

[19] M. Xu and L. Zhang, δ-homogeneity in Finsler geometry and the positive curvature problem, Osaka J. Math. 55 (2018), no. 1, 177–194. Search in Google Scholar

[20] M. Xu and W. Ziller, Reversible homogeneous Finsler metrics with positive flag curvature, Forum Math. 29 (2017), no. 5, 1213–1226. 10.1515/forum-2016-0173Search in Google Scholar