Invariant Metrics on the Complex Ellipsoid

被引:6
作者
Cho, Gunhee [1 ]
机构
[1] Univ Connecticut, Dept Math, 196 Auditorium Rd, Storrs, CT 06269 USA
关键词
Invariant metrics; Complex ellipsoid; Bergman metric; Kahler-Einstein metric; Kobayashi-Royden metric; Caratheodory-Reiffen metric; Geometric convex domain; Wu-Yau theorem; PSEUDOCONVEX DOMAINS; BOUNDARY-BEHAVIOR; CONVEX DOMAINS; KAHLER; CURVATURE;
D O I
10.1007/s12220-019-00333-w
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We provide a class of geometric convex domains on which the Caratheodory-Reiffen metric, the Bergman metric, the complete Kahler-Einstein metric of negative scalar curvature are uniformly equivalent, but not proportional to each other. In a two-dimensional case, we provide a full description of curvature tensors of the Bergman metric on the weakly pseudoconvex boundary point and show that invariant metrics are proportional to each other if and only if the geometric convex domain is the Euclidean ball.
引用
收藏
页码:2088 / 2104
页数:17
相关论文
共 20 条
[1]   STRICTLY PSEUDO-CONVEX DOMAINS IN CN [J].
BEALS, M ;
FEFFERMAN, C ;
GROSSMAN, R .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 8 (02) :125-322
[2]  
BLAND JS, 1986, MICH MATH J, V33, P209
[3]   ON THE EXISTENCE OF A COMPLETE KAHLER METRIC ON NON-COMPACT COMPLEX-MANIFOLDS AND THE REGULARITY OF FEFFERMANS EQUATION [J].
CHENG, SY ;
YAU, ST .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (04) :507-544
[4]  
Cho G, 2018, ARXIV180606311MATHDG
[5]   AN EXPLICIT COMPUTATION OF THE BERGMAN-KERNEL FUNCTION [J].
D'ANGELO, JP .
JOURNAL OF GEOMETRIC ANALYSIS, 1994, 4 (01) :23-34
[7]  
Fu SQ, 1997, MATH RES LETT, V4, P697
[8]  
GRAHAM I, 1975, T AM MATH SOC, V207, P219
[9]  
Huang X., 2016, ARXIV160407065MATHDG
[10]  
Jarnicki M., 2013, INVARIANT DISTANCES, DOI DOI 10.1515/9783110253863