Abstract
In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian.
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References
Akbar-Zadeh H. Sur les espaces de Finsler á courbures sectionnelles constantes. Acad Roy Belg Bull Cl Sci, 74: 281–322 (1988)
Kim C W, Yim J H. Finsler manifolds with positive constant flag curvature. Geom Dedicata, 98: 47–56 (2003)
Shen Z. Nonpositively curved Finsler manifolds with constant S-curvature. Math Z, 249: 625–639 (2005)
Shen Z. Lectures on Finsler Geometry. Singapore: World Sci, 2001
Chern S S, Shen Z. Riemannian-Finsler Geometry. Singapore: Worid Sci, 2005
Chern S S. Local equivlence and Euclidean connections in Finsler spaces. Sci Rep Nat TsingHua Univ Ser A, 5: 95–121 (1948)
Wu B Y. Some results on the geometry of tangent bundle of Finsler manifolds. Pub Math Debrecen, in press
Deiche A. Über die Finsler-Räume mit A i = 0. Arch Math, 4: 45–51 (1953)
Cheng X, Mo X, Shen Z. On the flag curvature of Finsler metrics of scalar curvature. J of London Math Soc, 68: 762–780 (2003)
Cheng X, Shen Z. Randers metrics with special curvature properties. Osaka J Math, 40: 87–101 (2003)
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This work was supported partially by the National Natural Science Foundation of China (Grant No. 10671214), the Natural Science Foundation of Fujian Province of China (Grant No. S0650024) and the Fund of the Education Department of Fujian Province of China (Grant No. JA06053)
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Wu, By. A global rigidity theorem for weakly Landsberg manifolds. SCI CHINA SER A 50, 609–614 (2007). https://doi.org/10.1007/s11425-007-0031-6
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DOI: https://doi.org/10.1007/s11425-007-0031-6