References

[1] J. C. Alvarez-Paiva, G. Berck, Finsler surfaces with prescribed geodesics, 2010. arXiv:1002.0243

[2] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, P. A. Griffiths, Exterior differential systems, Mathematical Sciences Research Institute Publications 18, Springer-Verlag, New York, 1991. MR

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

[4] R. L. Bryant, M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures, J. Differential Geom. 83 (2009), 465–499. MR zbM

[5] A. Čap, J. Slovák, Parabolic geometries. I, Mathematical Surveys and Monographs 154, American Mathematical Society, Providence, RI, 2009, Background and general theory. MR zbM

[6] E. Cartan, Sur les variétés à connexion projective, Bull. Soc. Math. France 52 (1924), 205–241. MR zbM

[7] 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

[8] M. Dunajski, L. J. Mason, P. Tod, Einstein-Weyl geometry, the dKP equation and twistor theory, J. Geom. Phys. 37 (2001), 63–93. MR

[9] M. Dunajski, P. Tod, Four-dimensional metrics conformal to Kähler, Math. Proc. Cambridge Philos. Soc. 148 (2010), 485–503. MR

[10] M. Eastwood, V. Matveev, Metric connections in projective differential geometry, in Symmetries and overdetermined systems of partial differential equations, IMA Vol. Math. Appl. 144, Springer, New York, 2008, pp. 339–350. MR zbM

[11] L. P. Eisenhart, O. Veblen, The Riemann geometry and its generalization, Proc. Nat. Acad. Sci. 8 (1922), 19–23.

[12] G. Gallavotti, D. Ruelle, SRB states and nonequilibrium statistical mechanics close to equilibrium, Comm. Math. Phys. 190 (1997), 279–285. MR

[13] W. Hoover, in Molecular dynamics, Lecture Notes in Phys 258, Springer, Berlin, 1986.

[14] T. A. Ivey, J. M. Landsberg, Cartan for beginners: differential geometry via moving frames and exterior differential systems, Graduate Studies in Mathematics 61, American Mathematical Society, Providence, RI, 2003. MR

[15] S. Kobayashi, T. Nagano, On projective connections, J. Math. Mech. 13 (1964), 215–235. MR zbM

[16] C. Lebrun, L. J. Mason, Zoll manifolds and complex surfaces, J. Differential Geom. 61 (2002), 453–535. MR zbM

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

[18] R. Liouville, Sur les invariants de certaines équations différentielles et sur leurs applications., C. R. Acad. Sci., Paris 109 (1889), 560–563. zbM

[19] V. S. Matveev, Geodesically equivalent metrics in general relativity, J. Geom. Phys. 62 (2012), 675–691. MR

[20] T. Mettler, Reduction of \(\beta\)-integrable 2-Segre structures, Comm. Anal. Geom. 21 (2013), 331–353. MR zbM

[21] A. Newlander, L. Nirenberg, Complex analytic coordinates in almost complex manifolds, Ann. of Math. (2) 65 (1957), 391–404. MR

[22] L. Nirenberg, Lectures on linear partial differential equations, American Mathematical Society, Providence, R.I., 1973. MR

[23] P. Nurowski, Projective versus metric structures, J. Geom. Phys. 62 (2012), 657–674. MR

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

[25] H. Pedersen, A. Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc. (3) 66 (1993), 381–399. MR

[26] T. Y. Thomas, On the projective and equi-projective geometries of paths., Proc. Nat. Acad. Sci. 11 (1925), 199–203. DOI

[27] H. Weyl, Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung., Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1921 (1921), 99–112 (German). zbM

[28] M. P. Wojtkowski, \(W\)-flows on Weyl manifolds and Gaussian thermostats, J. Math. Pures Appl. (9) 79 (2000), 953–974. MR