Geometry & Topology Volume 16, issue 4 (2012)

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

DOI: 10.2140/gt.2012.16.2135

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