Volume 16, issue 4 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
The Binet–Legendre Metric in Finsler Geometry

Vladimir S Matveev and Marc Troyanov

Geometry & Topology 16 (2012) 2135–2170
Bibliography
1 D V Alekseevskiĭ, Groups of conformal transformations of Riemannian spaces, Mat. Sb. 89(131) (1972) 280, 356 MR0334077
2 D Bao, On two curvature-driven problems in Riemann–Finsler geometry, from: "Finsler geometry, Sapporo 2005—in memory of Makoto Matsumoto" (editors S V Sabau, H Shimada), Adv. Stud. Pure Math. 48, Math. Soc. Japan (2007) 19 MR2389251
3 D Bao, S S Chern, Z Shen, An introduction to Riemann–Finsler geometry, Graduate Texts in Mathematics 200, Springer (2000) MR1747675
4 V N Berestovskiĭ, Generalized symmetric spaces, Sibirsk. Mat. Zh. 26 (1985) 3, 221 MR788325
5 M Berger, Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France 83 (1955) 279 MR0079806
6 H Busemann, The geometry of geodesics, Academic Press (1955) MR0075623
7 H Busemann, B B Phadke, Two theorems on general symmetric spaces, Pacific J. Math. 92 (1981) 39 MR618044
8 P Centore, Volume forms in Finsler spaces, Houston J. Math. 25 (1999) 625 MR1829124
9 S S Chern, Local equivalence and Euclidean connections in Finsler spaces, Sci. Rep. Nat. Tsing Hua Univ. Ser. A. 5 (1948) 95 MR0031812
10 S S Chern, Z Shen, Riemann–Finsler geometry, Nankai Tracts in Mathematics 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2005) MR2169595
11 G de Rham, Sur la reductibilité d'un espace de Riemann, Comment. Math. Helv. 26 (1952) 328 MR0052177
12 S Deng, Z Hou, The group of isometries of a Finsler space, Pacific J. Math. 207 (2002) 149 MR1974469
13 S Deng, Z Hou, Homogeneous Finsler spaces of negative curvature, J. Geom. Phys. 57 (2007) 657 MR2271210
14 S Deng, Z Hou, On symmetric Finsler spaces, Israel J. Math. 162 (2007) 197 MR2365860
15 J Ferrand, The action of conformal transformations on a Riemannian manifold, Math. Ann. 304 (1996) 277 MR1371767
16 P Foulon, Locally symmetric Finsler spaces in negative curvature, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 1127 MR1451935
17 D Fried, Closed similarity manifolds, Comment. Math. Helv. 55 (1980) 576 MR604714
18 P Hartman, Ordinary differential equations, John Wiley & Sons (1964) MR0171038
19 E Heil, D Laugwitz, Finsler spaces with similarity are Minkowski spaces, Tensor 28 (1974) 59 MR0355918
20 S Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics 80, Academic Press [Harcourt Brace Jovanovich Publishers] (1978) MR514561
21 S Ishihara, Homogeneous Riemannian spaces of four dimensions, J. Math. Soc. Japan 7 (1955) 345 MR0082717
22 C W Kim, Locally symmetric positively curved Finsler spaces, Arch. Math. (Basel) 88 (2007) 378 MR2311846
23 S Kobayashi, T Nagano, Riemannian manifolds with abundant isometries, from: "Differential geometry (in honor of Kentaro Yano)" (editors M Obata, S Kobayashi), Kinokuniya (1972) 195 MR0358623
24 N H Kuiper, Compact spaces with a local structure determined by the group of similarity transformations in $E^n$, Nederl. Akad. Wetensch., Proc. 53 (1950) 1178 MR0039248
25 R S Kulkarni, Conformally flat manifolds, Proc. Nat. Acad. Sci. U.S.A. 69 (1972) 2675 MR0307113
26 A M Legendre, Traité des fonctions elliptiques et des intégrales eulériennes, Volume 1, Huzard-Courcier (1825)
27 J Liouville, Extension au cas des trois dimensions de la question du tracé géographique, Applications de l'analyse à la géométrie (1850) 609
28 J Liouville, Théorème sur l'équation $dx^2+dy^2+dz^2 = \lambda (d\alpha^2 + d\beta^2 + d\gamma^2)$, J. Math. Pures et Appliquées (1850)
29 R L Lovas, J Szilasi, Homotheties of Finsler manifolds, SUT J. Math. 46 (2010) 23 MR2732642
30 E Lutwak, D Yang, G Zhang, A new ellipsoid associated with convex bodies, Duke Math. J. 104 (2000) 375 MR1781476
31 E Lutwak, D Yang, G Zhang, $L_p$ John ellipsoids, Proc. London Math. Soc. 90 (2005) 497 MR2142136
32 M Matsumoto, Conformally Berwald and conformally flat Finsler spaces, Publ. Math. Debrecen 58 (2001) 275 MR1807590
33 S Matsumoto, Foundations of flat conformal structure, from: "Aspects of low-dimensional manifolds" (editors Y Matsumoto, S Morita), Adv. Stud. Pure Math. 20, Kinokuniya (1992) 167 MR1208312
34 V S Matveev, Riemannian metrics having common geodesics with Berwald metrics, Publ. Math. Debrecen 74 (2009) 405 MR2521384
35 V S Matveev, H B Rademacher, M Troyanov, A Zeghib, Finsler conformal Lichnerowicz–Obata conjecture, Ann. Inst. Fourier (Grenoble) 59 (2009) 937 MR2543657
36 V D Milman, A Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed $n$–dimensional space, from: "Geometric aspects of functional analysis (1987–88)" (editors J Lindenstrauss, V D Milman), Lecture Notes in Math. 1376, Springer (1989) 64 MR1008717
37 D Montgomery, H Samelson, Transformation groups of spheres, Ann. of Math. 44 (1943) 454 MR0008817
38 P Planche, Géométrie de Finsler sur les espaces symétriques, Thèse Genève (1995)
39 P Planche, Structures de Finsler invariantes sur les espaces symétriques, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1455 MR1366100
40 R Schoen, On the conformal and CR automorphism groups, Geom. Funct. Anal. 5 (1995) 464 MR1334876
41 R Schoen, S T Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988) 47 MR931204
42 J Simons, On the transitivity of holonomy systems, Ann. of Math. 76 (1962) 213 MR0148010
43 Z I Szabó, Berwald metrics constructed by Chevalley's polynomials arXiv:math/0601522
44 Z I Szabó, Positive definite Berwald spaces, Structure theorems on Berwald spaces, Tensor 35 (1981) 25 MR614132
45 I Vaisman, C Reischer, Local similarity manifolds, Ann. Mat. Pura Appl. 135 (1983) 279 MR750537
46 C Vincze, A new proof of Szabó's theorem on the Riemann-metrizability of Berwald manifolds, Acta Math. Acad. Paedagog. Nyházi. 21 (2005) 199 MR2162616
47 H C Wang, On Finsler spaces with completely integrable equations of Killing, J. London Math. Soc. 22 (1947) 5 MR0022431
48 K Yano, On $n$–dimensional Riemannian spaces admitting a group of motions of order $n(n-1)/2+1$, Trans. Amer. Math. Soc. 74 (1953) 260 MR0052860