References

[1] A. Adem, J. Leida, Y. Ruan, Orbifolds and stringy topology, Cambridge Tracts in Mathematics 171, Cambridge University Press, Cambridge, 2007. MR

[2] H. Akbar-Zadeh, Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci. (5) 74 (1988), 281–322. MR

[3] M. Amann, C. Lange, M. Radeschi, Odd-dimensional orbifolds with all geodesics closed are covered by manifolds, 2018. arXiv:1811.10320

[4] A. L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas] 93, Springer-Verlag, Berlin-New York, 1978, With appendices by D. B. A. Epstein, J.-P. Bourguignon, L. Bérard-Bergery, M. Berger and J. L. Kazdan. MR

[5] M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 319, Springer-Verlag, Berlin, 1999. MR

[6] R. L. Bryant, P. Foulon, S. V. Ivanov, V. S. Matveev, W. Ziller, Geodesic behavior for Finsler metrics of constant positive flag curvature on \(S^2\), J. Differential Geom. 117 (2021), 1–22. MR

[7] R. L. Bryant, Finsler surfaces with prescribed curvature conditions, Unpublished manuscript, 1995.

[8] R. L. Bryant, Finsler structures on the \(2\)-sphere satisfying \(K=1\), in Finsler geometry (Seattle, WA, 1995), Contemp. Math. 196, Amer. Math. Soc., Providence, RI, 1996, pp. 27–41. MR

[9] R. L. Bryant, Projectively flat Finsler \(2\)-spheres of constant curvature, Selecta Math. (N.S.) 3 (1997), 161–203. MR

[10] R. L. Bryant, Some remarks on Finsler manifolds with constant flag curvature, Houston J. Math. 28 (2002), 221–262, Special issue for S. S. Chern. MR

[11] R. L. Bryant, Geodesically reversible Finsler 2-spheres of constant curvature, in Inspired by S. S. Chern, Nankai Tracts Math. 11, World Sci. Publ., Hackensack, NJ, 2006, pp. 95–111. MR

[12] R. L. Bryant, G. Manno, V. S. Matveev, A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields, Math. Ann. 340 (2008), 437–463. MR

[13] E. Cartan, Sur un problème d’équivalence et la théorie des espaces métriques généralisés., Mathematica 4 (1930), 114–136 (French).

[14] M. Dubois-Violette, Structures complexes au-dessus des variétés, applications, in Mathematics and physics (Paris, 1979/1982), Progr. Math. 37, Birkhäuser Boston, Boston, MA, 1983, pp. 1–42. MR

[15] D. B. A. Epstein, Periodic flows on three-manifolds, Ann. of Math. (2) 95 (1972), 66–82. MR

[16] P. Foulon, Curvature and global rigidity in Finsler manifolds, Houston J. Math. 28 (2002), 263–292, Special issue for S. S. Chern. MR

[17] H. Geiges, J. Gonzalo Pérez, Transversely holomorphic flows and contact circles on spherical 3-manifolds, Enseign. Math. 62 (2016), 527–567. MR

[18] H. Geiges, C. Lange, Seifert fibrations of lens spaces, Abh. Math. Semin. Univ. Hambg. 88 (2018), 1–22. MR

[19] N. J. Hitchin, Complex manifolds and Einstein’s equations, in Twistor geometry and nonlinear systems (Primorsko, 1980), Lecture Notes in Math. 970, Springer, Berlin-New York, 1982, pp. 73–99. MR

[20] Y. Imayoshi, M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag, Tokyo, 1992, Translated and revised from the Japanese by the authors. MR

[21] T. A. Ivey, J. M. Landsberg, Cartan for beginners, Graduate Studies in Mathematics 175, American Mathematical Society, Providence, RI, 2016, Second edition. MR

[22] A. B. Katok, Ergodic perturbations of degenerate integrable Hamiltonian systems, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 539–576. MR

[23] S. Kobayashi, Transformation groups in differential geometry, Classics in Mathematics, Springer-Verlag, Berlin, 1995, Reprint of the 1972 edition. MR

[24] C. Lange, On metrics on 2-orbifolds all of whose geodesics are closed, J. Reine Angew. Math. 758 (2020), 67–94. MR

[25] C. Lange, Orbifolds from a metric viewpoint, Geom. Dedicata 209 (2020), 43–57. MR

[26] C. R. LeBrun, Spaces of complex geodesics and related structures, Ph.D. thesis, University of Oxford, Bodleian Library Oxford, 1980, available at https://ora.ox.ac.uk/objects/uuid:e29dd99c-0437-4956-8280-89dda76fa3f8.

[27] C. R. LeBrun, L. J. Mason, Zoll manifolds and complex surfaces, J. Differential Geom. 61 (2002), 453–535. MR

[28] C. R. LeBrun, L. J. Mason, Zoll metrics, branched covers, and holomorphic disks, Comm. Anal. Geom. 18 (2010), 475–502. MR

[29] V. S. Matveev, Lichnerowicz-Obata conjecture in dimension two, Comment. Math. Helv. 80 (2005), 541–570. MR

[30] V. S. Matveev, Proof of the projective Lichnerowicz-Obata conjecture, J. Differential Geom. 75 (2007), 459–502. MR

[31] T. Mettler, Weyl metrisability of two-dimensional projective structures, Math. Proc. Cambridge Philos. Soc. 156 (2014), 99–113. MR

[32] T. Mettler, Geodesic rigidity of conformal connections on surfaces, Math. Z. 281 (2015), 379–393. MR

[33] T. Mettler, G. P. Paternain, Holomorphic differentials, thermostats and Anosov flows, Math. Ann. 373 (2019), 553–580. MR

[34] T. Mettler, G. P. Paternain, Convex projective surfaces with compatible Weyl connection are hyperbolic, Anal. PDE 13 (2020), 1073–1097. MR

[35] N. R. O’Brian, J. H. Rawnsley, Twistor spaces, Ann. Global Anal. Geom. 3 (1985), 29–58. MR

[36] I. Satake, The Gauss-Bonnet theorem for \(V\)-manifolds, J. Math. Soc. Japan 9 (1957), 464–492. MR

[37] P. Scott, The geometries of \(3\)-manifolds, Bull. London Math. Soc. 15 (1983), 401–487. MR

[38] H. Seifert, Topologie Dreidimensionaler Gefaserter Räume, Acta Math. 60 (1933), 147–238. MR

[39] W. P. Thurston, The geometry and topology of three-manifolds, 1979, Lecture Notes, Princeton University.

[40] S. Zhu, Critical metrics on \(2\)-dimensional orbifolds, Indiana Univ. Math. J. 46 (1997), 1273–1288. MR

[41] W. Ziller, Geometry of the Katok examples, Ergodic Theory Dynam. Systems 3 (1983), 135–157. MR

[42] O. Zoll, Ueber Flächen mit Scharen geschlossener geodätischer Linien, Math. Ann. 57 (1903), 108–133. MR