COMPLEX BERWALD MANIFOLDS WITH VANISHING HOLOMORPHIC SECTIONAL CURVATURE*
Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 203-208

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we prove that a strongly convex and Kähler-Finsler metric is a complex Berwald metric with zero holomorphic sectional curvature if and only if it is a complex locally Minkowski metric.
DOI : 10.1017/S001708950800414X
Mots-clés : 53C56, 32Q99
YAN, RONGMU. COMPLEX BERWALD MANIFOLDS WITH VANISHING HOLOMORPHIC SECTIONAL CURVATURE*. Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 203-208. doi: 10.1017/S001708950800414X
@article{10_1017_S001708950800414X,
     author = {YAN, RONGMU},
     title = {COMPLEX {BERWALD} {MANIFOLDS} {WITH} {VANISHING} {HOLOMORPHIC} {SECTIONAL} {CURVATURE*}},
     journal = {Glasgow mathematical journal},
     pages = {203--208},
     year = {2008},
     volume = {50},
     number = {2},
     doi = {10.1017/S001708950800414X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950800414X/}
}
TY  - JOUR
AU  - YAN, RONGMU
TI  - COMPLEX BERWALD MANIFOLDS WITH VANISHING HOLOMORPHIC SECTIONAL CURVATURE*
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 203
EP  - 208
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950800414X/
DO  - 10.1017/S001708950800414X
ID  - 10_1017_S001708950800414X
ER  - 
%0 Journal Article
%A YAN, RONGMU
%T COMPLEX BERWALD MANIFOLDS WITH VANISHING HOLOMORPHIC SECTIONAL CURVATURE*
%J Glasgow mathematical journal
%D 2008
%P 203-208
%V 50
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950800414X/
%R 10.1017/S001708950800414X
%F 10_1017_S001708950800414X

[1] 1.Abate, M. and Patrizio, G.Finsler metric-a global approach. Lecture Notes in Mathematics No. 1591, (Springer-Verlag, 1994). Google Scholar | DOI

[2] 2.Bao, D., Chern, S.S. and Shen, Z.An introduction to Riemann-Finsler geometry (Springer-Verlag, 2000). Google Scholar | DOI

[3] 3.Chern, S.S. and Shen, Z.Riemann-Finsler geometry (Worldscientific, Singapore, 2005). Google Scholar | DOI

[4] 4.Shen, Z.Volume comparison and its applications in Riemann-Finsler Geometry, Adv. Math. 128, 306–328 (1997). Google Scholar | DOI

[5] 5.Szabó, Z.Positive definite Berwald spaces (Structure Theorems on Berwald spaces), Tensor, N.S. 35 (1981), 25–39. Google Scholar

[6] 6.Xiao, J. and Yan, R.Two topics in complex Finsler geometry, J. Xiamen Daxue Xuebao Ziran Kexue Ban 45 (2006), 614–616. Google Scholar

[7] 7.Yan, R.Connections on complex Finsler manifold, Acta Math. Applie. Sinica 19, 431–436 (2003). Google Scholar | DOI

[8] 8.Yan, R.On the volume of the projectivized tangent bundle in a complex Finsler manifold, Arch Math. 86, 458–463 (2006). Google Scholar | DOI

[9] 9.Yan, R., Holomorphic sectional curvature in complex Finsler Geometry. Preprint. Google Scholar

Cité par Sources :