Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NOTE ON THE GENERALIZED MYERS THEOREM FOR FINSLER MANIFOLDS

  • Wu, Bing-Ye (Department of Mathematics Minjiang University)
  • Received : 2012.03.09
  • Published : 2013.05.31
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Abstract

In this note we establish a generalized Myers theorem under line integral curvature bound for Finsler manifolds.

Keywords

References

  1. D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Ggeometry, GTM 200, Springer-Verlag, 2000.
  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
  3. 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
  4. Z. Shen, Lectures on Finsler Geometry, World Sci., 2001, Singapore.
  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
  6. B. Y.Wu and Y. L. Xin, Comparison theorems in Finsler geometry and their applications, Math. Ann. 337 (2007), no. 1, 177-196.
  7. 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

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  1. Two Compactness Theorems on Finsler Manifolds with Positive Weighted Ricci Curvature vol.72, pp.1-2, 2017, https://doi.org/10.1007/s00025-017-0673-9
  2. A Bound of the Finslerian Ricci Scalar vol.15, pp.3, 2018, https://doi.org/10.1007/s00009-018-1180-2