Characterization of Holomorphic Invariant Complex Finsler Metrics and Schwarz Lemma on the Polyball

被引:0
作者
Lin, Shuqing [1 ]
Wang, Ruiwen [1 ]
Zhong, Chunping [1 ]
机构
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
基金
中国国家自然科学基金;
关键词
Invariant metric; K & auml; hler-Berwald metric; Holomorphic sectional curvature; Schwarz lemma;
D O I
10.1007/s12220-024-01713-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A domain B subset of CN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pmb {B}\subset \mathbb {C}<^>N$$\end{document} is called a polyball if it is given as a direct product of open unit balls. We prove that every holomorphic invariant strongly pseudoconvex complex Finsler metric F:T1,0B ->[0,+infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F:T<^>{1,0}\pmb {B}\rightarrow [0,+\infty )$$\end{document} on a polyball B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pmb {B}$$\end{document} is necessary a K & auml;hler-Berwald metric with the holomorphic sectional curvature bounded between two negative constants, and its holomorphic bisectional curvature is nonpositive and bounded from below by a negative constant. These important curvature properties make it possible for us to establish a Schwarz lemma for holomorphic mappings f from a polyball B1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pmb {B}_1$$\end{document} into another polyball B2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pmb {B}_2$$\end{document} whenever they are endowed with arbitrary holomorphic invariant K & auml;hler-Berwald metrics which are not necessary Hermitian quadratic.
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页数:32
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共 30 条
[1]  
Abate M., 1994, Lecture Notes in Mathematics (LNM, V1591, DOI [10.1007/BFB0073980, DOI 10.1007/BFB0073980]
[2]   An extension of Schwarz's lemma [J].
Ahlfors, Lars V. .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1938, 43 (1-3) :359-364
[3]   Complex manifolds modeled on a complex Minkowski space [J].
Aikou, T .
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1995, 35 (01) :85-103
[4]   Kahler Finsler Metrics Are Actually Strongly Kahler [J].
Chen, Bin ;
Shen, Yibing .
CHINESE ANNALS OF MATHEMATICS SERIES B, 2009, 30 (02) :173-178
[5]  
CHEN Z, 1979, SCI SINICA, V22, P1238
[6]  
Chern S-S., 2000, An Introduction to Riemann-Finsler Geometry, DOI [DOI 10.1007/978-1-4612-1268-3, 10.1007/978-1-4612-1268-3]
[7]   Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains [J].
Ge, Xiaoshu ;
Zhong, Chunping .
SCIENCE CHINA-MATHEMATICS, 2024, 67 (08) :1827-1864
[8]  
Kim KT., 2011, Schwarzs Lemma from a Differential Geometric Viewpoint
[9]   DISTANCE HOLOMORPHIC MAPPINGS AND SCHWARZ LEMMA [J].
KOBAYASHI, S .
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1967, 19 (04) :481-+
[10]   An intrinsic characterization of the direct product of balls [J].
Kodama, Akio ;
Shimizu, Satoru .
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2009, 49 (03) :619-630