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CHARACTERIZING COMPLEX LOCALLY MINKOWSKI SPACES BY HOLOMORPHIC SECTIONAL CURVATURE

  • Chen, Xinxiang (School of Mathematical Science Xiamen University) ;
  • Yan, Rongmu (School of Mathematical Science Xiamen University)
  • Received : 2010.01.01
  • Published : 2012.01.31

Abstract

In this paper, we prove that a complex Finsler manifold is a complex locally Minkowski space if and only if it is a strictly K$\ddot{a}$hler-Berwald manifold with zero holomorphic sectional curvature.

Keywords

References

  1. M. Abate and G. Patrizio, Finsler Metrics-A Global Approach, with applications to geometric function theory, Lecture Notes in Mathematics, 1591. Springer-Verlag, Berlin, 1994.
  2. T. Aikou, On complex Finsler manifolds, Rep. Fac. Sci. Kagoshima Univ. Math. Phys. Chem. (1991), no. 24, 9-25.
  3. N. Aldea, The holomorphic bisectional curvature of the complex Finsler spaces, Novi Sad J. Math. 35 (2005), no. 2, 143-153.
  4. D. Bao, S. S. Chern, and Z. Shen, An Introduction to Riemann-Finsler Geometry, GTM 200, Springer-Verlag, New York, 2000.
  5. Y. Chen and R. Yan, The Szabo metric on product of complex manifolds, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 4, 801-804.
  6. S. S. Chern and Z. Shen, Riemann-Finsler Geometry, World scientific, Singapore, 2005.
  7. Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv. Math. 128 (1997), no. 2, 306-328. https://doi.org/10.1006/aima.1997.1630
  8. Z. Szabo, Positive definite Berwald spaces. Structure theorems on Berwald spaces, Tensor (N.S.) 35 (1981), no. 1, 25-39.
  9. J. Xiao and R. Yan, Two topics in complex Finsler geometry, Xiamen Daxue Xuebao Ziran Kexue Ban 45 (2006), no. 5, 614-616.
  10. R. Yan, Connections on complex Finsler manifold, Acta Math. Appl. Sin. Engl. Ser. 19 (2003), no. 3, 431-436. https://doi.org/10.1007/s10255-003-0118-y
  11. R. Yan, On the volume of the projectivized tangent bundle in a complex Finsler manifold, Arch. Math. (Basel) 86 (2006), no. 5, 458-463. https://doi.org/10.1007/s00013-005-1498-4
  12. R. Yan, Holomorphic sectional curvature in complex Finsler geometry, Preprint.
  13. R. Yan, Complex Berwald manifolds with vanishing holomorphic sectional curvature, Glasg. Math. J. 50 (2008), no. 2, 203-208.
  14. R. Yan, Complex Berwald manifolds with vanishing holomorphic sectional curvature-corrigendum, Glasg. Math. J. 52 (2010), no. 1, 205. https://doi.org/10.1017/S001708950999036X