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CHARACTERIZING COMPLEX LOCALLY MINKOWSKI SPACES BY HOLOMORPHIC SECTIONAL CURVATURE
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 Title & Authors
CHARACTERIZING COMPLEX LOCALLY MINKOWSKI SPACES BY HOLOMORPHIC SECTIONAL CURVATURE
Chen, Xinxiang; Yan, Rongmu;
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 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 Khler-Berwald manifold with zero holomorphic sectional curvature.
 Keywords
complex Berwald manifold;holomorphic sectional curvature;complex locally Minkowski space;
 Language
English
 Cited by
 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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)