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Affinely equivalent Kähler-Finsler metrics on a complex manifold

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Abstract

The purpose of the present paper is to investigate affinely equivalent Kähler-Finsler metrics on a complex manifold. We give two facts (1) Projectively equivalent Kähler-Finsler metrics must be affinely equivalent; (2) a Kähler-Finsler metric is a Kähler-Berwald metric if and only if it is affinely equivalent to a Kähler metric. Furthermore, we give a formula to describe the affine equivalence of two weakly Kähler-Finsler metrics.

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References

  1. Abate M, Patrizio G. Finsler metric-A global approach. Lecture Notes in Math, vol. 1591. Berlin: Springer-Verlag, 1994

    Google Scholar 

  2. Aikou T. On complex Finsler manifold. Math Phys Chem, 1991, 24: 9–25

    MathSciNet  MATH  Google Scholar 

  3. Chen B, Shen Y. Kähler Finsler metrics are actually strongly Kähler. Chin Ann Math Ser B, 2009, 30: 173–178

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen Y, Yan R. The Szabó metric on product of complex manifolds. Acta Math Sin Engl Ser, 2007, 50: 801–804

    MathSciNet  MATH  Google Scholar 

  5. Chern S S, Shen Z. Riemann-Finsler Geometry. WorldScientific, 2005

  6. Goldberg S I. Curvature and Homology. New York: Academic Press, 1962

    MATH  Google Scholar 

  7. Rapcrá K A. Über die bahntreuen Abbildungen metrischer Räume. Publ Math Debrecen, 1961, 8: 285–290

    MathSciNet  Google Scholar 

  8. Shen Z. Volume comparison and its applications in Riemann-Finsler geometry. Adv Math, 1997, 128: 306–328

    Article  MathSciNet  MATH  Google Scholar 

  9. Szabó Z. Positive definite Berwald spaces (Structure Theorems on Berwald spaces). Tensor N S, 1981, 35: 25–39

    MathSciNet  MATH  Google Scholar 

  10. Yan R. Connections on complex Finsler manifold. Acta Mathematicae Applicatae Sinica, 2003, 3: 431–436

    Google Scholar 

  11. Yan R. On the volume of the projectivized tangent bundle in a complex Finsler manifold. Arch Math, 2006, 86:458–463

    Article  MATH  Google Scholar 

  12. Yan R. Complex Berwald manifolds with vanishing holomorphic sectional curvature. Glasgow Math J, 2008, 50:203–208

    Article  MATH  Google Scholar 

Download references

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  1. School of Mathematical Science, Xiamen University, Xiamen, 361005, China

    RongMu Yan

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  1. RongMu Yan
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Correspondence to RongMu Yan.

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Yan, R. Affinely equivalent Kähler-Finsler metrics on a complex manifold. Sci. China Math. 55, 731–738 (2012). https://doi.org/10.1007/s11425-011-4343-1

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  • DOI: https://doi.org/10.1007/s11425-011-4343-1

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