- Volume 50 Issue 3
In this note we establish a generalized Myers theorem under line integral curvature bound for Finsler manifolds.
Myers theorem;Ricci curvature;Finsler manifold
- D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Ggeometry, GTM 200, Springer-Verlag, 2000.
- 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
- G. J. Galloway, A generalization of Myers' theorem and an application to relativistic cosmology, J. Differential Geom. 14 (1979), no. 1, 105-116. https://doi.org/10.4310/jdg/1214434856
- Z. Shen, Lectures on Finsler Geometry, World Sci., 2001, Singapore.
- 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
- B. Y.Wu and Y. L. Xin, Comparison theorems in Finsler geometry and their applications, Math. Ann. 337 (2007), no. 1, 177-196.
- 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
Supported by : Natural Science Foundation of China