Uniform Finsler Hadamard manifolds

Egloff, Daniel

Annales de l'I.H.P. Physique théorique, Tome 66 (1997) no. 3, pp. 323-357.

[1] M.T. Anderson and R. Schoen, Positive Harmonic Functions on Complete Manifolds of Negative Curvature, Annals of Math., Vol. 121, 1985, pp. 429-461. | MR | Zbl

[2] P.L. Antonelli, R.S. Ingarden and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluver Academic Pub., 1993. | MR | Zbl

[3] G.S. Asanov, Finsler Geometry, Relativity and Gauge Theories, D. Reidel, 1985. | MR | Zbl

[4] L. Auslander, On Curvature in Finsler Geometry, Trans. Amer. Math. Soc., Vol. 79, 1955, pp. 378-388. | MR | Zbl

[5] W. Ballmann, M. Gromov and V. Schroeder, Manifolds of Nonpositive Curvature, Progr. in Math., Vol. 61, Birkhäuser 1985. | MR | Zbl

[6] D. Bao and S.S. Chern, On a Notable Connection in Finsler Geometry, Houston J. of Math. Vol. 19, No. 1, 1993, pp. 135-180. | MR | Zbl

[7] Berestovkij V.N. and I.G. Nikolaev, Multidimensional Generalized Riemannian Spaces, Geometry IV, Encyclop. of Math. Sciences, Vol. 70, Springer, 1993. | MR | Zbl

[8] L. Berwald, Über die n-dimensionalen Geometrien konstanter Krümmung bei denen die Geraden die Kürzesten sind, Math. Zeitschr., Vol. 30, 1930, pp. 449-469. | JFM

[9] L. Berwald, Über Finslersche und Cartansche Geometrie I, Mathematica, Vol. 17, 1941, pp. 34-58. | JFM | MR

[10] Yu.D. Burago, M. Gromov and G. Perelman, A. D. Alekandrov's Space with Curvature bounded from below I, preprint.

[11] H. Busemann, The Geometry of Geodesics, Academic Press, New York, 1955. | MR | Zbl

[12] H. Busemann, Intrinsic Area, Ann. Math., Vol. 48, 1947, pp. 234-267. | MR | Zbl

[13] H. Busemann, Spaces with Non-Positive Curvature, Acta Math., Vol. 80, 1948, pp. 259-310. | MR | Zbl

[14] H. Busemann, Recent Synthetic Differential Geometry, Ergeb. der Math. und ihrer Grenzgebiete, Vol. 54, Springer, 1970. | MR | Zbl

[15] H. Busemann, Timelike Spaces, Dissert. Math, No. 53, 1967. | EuDML | MR | Zbl

[16] H. Busemann, Problem IV, Desarguesian Spaces; in Mathematical Developments arising from Hilbert Problems, Proc. Symp. in Pure Math, Vol. 28, 1976, pp. 131-141 | MR | Zbl

[17] H. Busemann, Quasi-Hyperbolic Geometry, Rend. Circ. Matem. Palermo, Serie II, IV, 1955, pp. 1-14.

[18] H. Busemann and W. Mayer, On the Foundations of Calculus of Variations, Trans. Amer. Math. Soc., Vol. 49, 1941, pp. 173-198. | JFM | MR | Zbl

[19] H. Busemann and J.P. Kelly, Projective Geometry and Projective Metrics, Academic Press, New York, 1953. | MR | Zbl

[20] H. Busemann and B.B. Phadke, Spaces with Distinguished Geodesics, Monographs and Textbooks in Pure and Appl. Math., No. 108, 1987. | MR | Zbl

[21] H. Busemann and B.B. Phadke, Two Theorems on General Symmetric Spaces, Pacific J. of Math., Vol. 92, 1981, pp. 39-48. | MR | Zbl

[22] E. Cartan, Les espaces de Finsler, Actualités Scientifiques et Industrielles, No. 79, Paris, Hermann, 1934. | JFM | Zbl

[23] P. Dazord, Propriétés globales des géodésiques des espaces de Finsler, Thèse No. 575, Publ. Math., Lyon, 1969.

[24] P. Eberlein, Geodesic Flow in certain Manifolds without Conjugate Points, Trans. Amer. Math. Soc., Vol. 167, 1972, pp. 151-170. | MR | Zbl

[25] P. Eberlein and B. O'Neill, Visibility Manifolds, Pacific J. Math., Vol. 46, 1973, pp. 45-109. | MR | Zbl

[26] D. Egloff, Some New Developments in Finsler Geometry, Dissertation, Univ. Fribourg, 1995.

[27] D. Egloff, On the Dynamics of Uniform Finsler Manifolds of Negative Flag Curvature, Preprint, Univ. Fribourg, 1995. | MR

[28] D. Egloff, Hilbert Geometries, Preprint, Univ. Fribourg, 1996.

[29] P. Finsler, Über Kurven und Flächen in allgemeinen Räumen, Birkhäuser Verlag, Basel, 1951. | MR | Zbl

[30] P. Foulon, Géométrie des équations différentielles du second ordre, Ann. Inst. Henri Poincaré, Vol. 45, No. 1 1986, pp. 1-28. | EuDML | Numdam | MR | Zbl

[31] P. Foulon, Réductibilité de systèmes dynamiques variationnels, Ann. Inst. Henri Poincaré, Vol. 45, No. 4, 1986, pp. 359-388. | EuDML | Numdam | MR | Zbl

[32] P. Foulon, Estimation de l'entropie des systèmes lagrangiens sans points conjugués, Ann. Inst. Henri Poincaré, Vol. 57, No. 2, 1992, pp. 117-146. | EuDML | Numdam | MR | Zbl

[33] P. Foulon, Cours de troisième cycle, École Polytechnique Palaiseau, 1992.

[34] P. Funk, Über Geometrien bei denen die Geraden die Kürzesten sind, Math. Annalen, Vol. 101, 1929, pp. 226-237. | EuDML | JFM | MR

[35] J. Grifone, Structure presque-tangente et connexions, I and II, Ann. Inst. Fourier, Vol. 22, No. 1, 1972, pp. 287-334, No. 3, 1972, pp. 291-338. | EuDML | Numdam | MR | Zbl

[36] M. Gromov, J. Lafontaine and P. Pansu, Structure métriques pour les variétés Riemanniennes, Cedic/Fernand Nathan, Paris, 1981. | MR | Zbl

[37] E. Heintze and H.C. Im Hof, Geometry of Horospheres, J. Diff. Geom., Vol. 12, 1977, pp. 481-491. | MR | Zbl

[38] E. Kann, Bonnet's Theorem in two-dimensional G-Spaces, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 765-784. | MR | Zbl

[39] A.B. Katok, Ergodic Properties of Degenerate Integrable Hamiltonian Systems, Math. USSR-Izv., Vol. 7, 1973, pp. 535-571. | Zbl

[40] P. Kelly and E.G. Straus, Curvature in Hilbert Geometry, Pacific J. Math., Vol. 8, 1958, pp. 119-125. | MR | Zbl

[41] W. Klingenberg, Geodätischer Fluss auf Mannigfaltikeiten vom hyperbolischen Typ, Invent. Math., Vol. 14, 1971, pp. 63-82. | EuDML | MR | Zbl

[42] F.P. Pedersen, On Space with Negative Curvature, Mat. Tidsskrift B, 1952, pp. 66-89. | MR | Zbl

[43] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall Inc., 1964. | MR | Zbl

[44] W. Ziller, Geometry of the Katok Examples, Ergod. Th. and Dynam. Sys., Vol. 3, 1983, pp. 135-157. | MR | Zbl