Browse > Article
http://dx.doi.org/10.14403/jcms.2020.33.1.1

HARMONIC FINSLER METRICS ON SPHERES  

Kim, Chang-Wan (Division of Liberal Arts and Sciences Mokpo National Maritime University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.33, no.1, 2020 , pp. 1-7 More about this Journal
Abstract
In this paper, it is shown that the reversible harmonic Finsler metrics on spheres must be Riemannian.
Keywords
Finsler metrics; Blaschke; harmonic; spheres;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 A. Abbondandolo, B. Bramham, U. L. Hryniewicz, and P. A. S. Salomao, Sharp systolic inequalities for Riemannian and Finsler spheres of revolution, preprint, available at arXiv:math/1808.06995 (2018).
2 J. C. Alvarez Paiva, Asymmetry in Hilbert's fourth problem, preprint, available at arXiv:math/1301.2524 (2013).
3 A. L. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik und ihrer Grenzgebiete 93, Springer-Verlag 1978.
4 R. L. Bryant, Geodesically reversible Finsler 2-spheres of constant curvature, Inspired by S. S. Chern, Nankai Tracts Math., 11 (2006), 95-111.
5 D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry, Graduate Studies in Mathematics 33, American Mathematical Society 2001.
6 C. E. Duran, A volume comparison theorem for Finsler manifolds, Proc. Amer. Math. Soc., 126 (1998), 3079-3082.   DOI
7 N. Innami, Y. Itokawa, T. Nagano, and K. Shiohama, Blaschke Finsler manifolds and actions or projective Randers changes on cut loci, Trans. Amer. Math. Soc., 371 (2019), 7433-7450.   DOI
8 S. Ivanov, Filling minimality of Finslerian 2-discs, Proc. Steklov Inst. Math., 273 (2011), 176-190.   DOI
9 K. Kiyohara, S. V. Sabau, and K. Shibuya, The geometry of a positively curved Zoll surface of revolution, Int. J. Geom. Methods Mod. Phys., 16 (2019), no. 02, 1941003.   DOI
10 C.-W. Kim, Locally symmetric positively curved Finsler spaces, Arch. Math., 88 (2007), 378-384.   DOI
11 C.-W. Kim, Harmonic Finsler manifolds with minimal horospheres, Commun. Korean Math. Soc., 33 (2018), 929-933.   DOI
12 R. L. Bryant, P. Foulon, S. Ivanov, V. S. Matveev, and W. Ziller, Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$, to appear J. Differential Geom.
13 C.-W. Kim, Blaschke Finsler metrics on spheres, Int. J. Geom. Methods Mod. Phys., 16 (2019), no. 9, 9 pages.
14 C.-W. Kim and J.-W. Yim, Finsler manifolds with positive constant flag curvature, Geom. Dedicata, 98 (2003), 47-56.   DOI
15 M. Matsumoto, Theory of curves in tangent planes of two-dimensional Finsler spaces, Tensor (N.S.) 37 (1982), 35-42.
16 S. Sabourau, Strong deformation retraction of the space of Zoll Finsler projective planes, J. Symplectic Geom., 17 (2019), 443-476.   DOI
17 Z. Shen, Volume comparison and its applications in Riemannian-Finsler geometry, Adv. Math., 128 (1997), 306-328.   DOI
18 Y.-B. Shen and Z. Shen, Introduction to modern Finsler geometry, World Scientific 2006.
19 K. Shiohama and B. Tiwari, The global study of Riemannian-Finsler geometry, Geometry in History, Springer-Verlag, (2019), 581-621.