[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b180636

GENERALIZED MYERS THEOREM FOR FINSLER MANIFOLDS WITH INTEGRAL RICCI CURVATURE BOUND

Wu, Bing-Ye (Institution of Mathematics Minjiang University)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 841-852 More about this Journal

Abstract

We establish the generalized Myers theorem for Finsler manifolds under integral Ricci curvature bound. More precisely, we show that the forward complete Finsler n-manifold whose part of Ricci curvature less than a positive constant is small in $L^p$ -norm (for p > n/2) have bounded diameter and finite fundamental group.

Keywords

extreme volume form; Finsler manifold; Ricci curvature; uniformity constant; fundamental group;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	D. Bao, S.-S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, Graduate Texts in Mathematics, 200, Springer-Verlag, New York, 2000. https://doi.org/10.1007/978-1-4612-1268-3
2	C. Chicone and P. Ehrlich, Line integration of Ricci curvature and conjugate points in Lorentzian and Riemannian manifolds, Manuscripta Math. 31 (1980), no. 1-3, 297-316. https://doi.org/10.1007/BF01303279 DOI
3	P. Petersen and C. Sprouse, Integral curvature bounds, distance estimates and applications, J. Differential Geom. 50 (1998), no. 2, 269-298. http://projecteuclid.org/euclid.jdg/1214461171 DOI
4	Y. Shen and W. Zhao, On fundamental groups of Finsler manifolds, Sci. China Math. 54 (2011), no. 9, 1951-1964. https://doi.org/10.1007/s11425-011-4233-6 DOI
5	B.-Y. Wu, Volume form and its applications in Finsler geometry, Publ. Math. Debrecen 78 (2011), no. 3-4, 723-741. https://doi.org/10.5486/PMD.2011.4998 DOI
6	B.-Y. Wu, On integral Ricci curvature and topology of Finsler manifolds, Internat. J. Math. 23 (2012), no. 11, 1250111, 26 pp. https://doi.org/10.1142/S0129167X1250111X DOI
7	B.-Y. Wu, A note on the generalized Myers theorem for Finsler manifolds, Bull. Korean Math. Soc. 50 (2013), no. 3, 833-837. https://doi.org/10.4134/BKMS.2013.50.3.833 DOI
8	E. Aubry, Finiteness of ${\pi}_1$ and geometric inequalities in almost positive Ricci curvature, Ann. Sci. Ecole Norm. Sup. (4) 40 (2007), no. 4, 675-695. https://doi.org/10.1016/j.ansens.2007.07.001 DOI
9	B.-Y. Wu, Comparison Theorems and Submanifolds in Finsler Geometry, Science Press Beijing, 2015.
10	J.-G. Yun, A note on the generalized Myers theorem, Bull. Korean Math. Soc. 46 (2009), no. 1, 61-66. https://doi.org/10.4134/BKMS.2009.46.1.061 DOI