典型文献
Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds
文献摘要：
Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ? Q.In terms of the Harish-Chandra realization Ω(∈)Cn and taking S to pass through the origin 0 ∈ Ω,so that S=E ∩ Ωfor some complex vector subspace of Cn,the author shows that the orthogonal projectionρ:Ω → E maps Ω onto S,and deduces that S C Ω is a holomorphic isometry with respect to the Carathéodory metric.His first theorem gives a new derivation of a result of Yeung's deduced from the classification theory by Satake and Ihara in the special case of totally geodesic complex submanifolds of rank 1 and of complex dimension≥2 in the Siegel upper half plane Hg,a result which was crucial for proving the nonexistence of totally geodesic complex suborbifolds of dimension≥2 on the open Torelli locus of the Siegel modular variety Ag by the same author.The proof relies on the characterization of totally geodesic submanifolds of Riemannian symmetric spaces in terms of Lie triple systems and a variant of the Hermann Convexity Theorem giving a new characterization of the Harish-Chandra realization in terms of bisectional curvatures.
文献关键词：
中图分类号：
作者姓名：
Ngaiming MOK
作者机构：
Department of Mathematics,The University of Hong Kong,Pokfulam Road,Hong Kong
文献出处：
引用格式：
[1]Ngaiming MOK-.Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds)[J].数学年刊B辑（英文版）,2022(06):1125-1142
A类：
Holomorphic,Retractions,Submanifolds,Harish,Satake,Ihara,suborbifolds,Torelli,bisectional
B类：
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AB值：
0.567249
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