Browse > Article
http://dx.doi.org/10.14403/jcms.2017.30.4.369

ON EXISTENCE AND DISTRIBUTION OF CONJUGATE POINTS IN FINSLER GEOMETRY  

Kim, Chang-Wan (Division of Liberal Arts and Sciences Mokpo National Maritime University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.30, no.4, 2017 , pp. 369-379 More about this Journal
Abstract
In this paper, we shall study the existence and distribution of conjugate points in Finsler geometry from the viewpoint of the oscillation and Morse index theory.
Keywords
Finsler metrics; conjugate points; Ricci curvature;
Citations & Related Records
연도 인용수 순위
  • Reference
1 W. Ambrose, A theorem of Myers, Duke Math. J. 24 (1957), 345-348.   DOI
2 M. Anastasiei, Galloways compactness theorem on Finsler manifolds, Balkan J. Geom. Appl. 20 (2015), 1-8.
3 L. Auslander, On curvature in Finsler geometry, Trans. Amer. Math. Soc. 79 (1955), 378-388.   DOI
4 D. Bao, S. S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, Graduate Texts in Mathematics, 200, Springer-Verlag, 2000.
5 G. J. Galloway, Compactness criteria for Riemannian manifolds, Proc. Amer. Math. Soc. 84 (1982), 106-110.   DOI
6 C.-W. Kim, Finsler manifolds without conjugate points and with integral Ricci curvature, Israel J. Math. 189 (2012), 135-146.   DOI
7 D. Kupeli, On existence and comparison of conjugate points in Riemannian and Lorentzian geometry, Math. Ann. 276 (1986), 67-79.   DOI
8 P. Mastrolia, M. Rimoldi, and G. Veronelli, Myers-type theorems and some related oscillation results, J. Geom. Anal. 22 (2012), 763-779.   DOI
9 S. Pigola, M. Rigoli, and A. G. Setti, Vanishing and finiteness results in geometric analysis, Progress in Mathematics, 266, Birkhauser, 2008.