Vol. 295, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the structure of holomorphic isometric embeddings of complex unit balls into bounded symmetric domains

Shan Tai Chan

Vol. 295 (2018), No. 2, 291–315
Abstract

We study general properties of holomorphic isometric embeddings of complex unit balls Bn into bounded symmetric domains of rank 2. In the first part, we study holomorphic isometries from (Bn ,kgBn) to (Ω,gΩ) with nonminimal isometric constants k for any irreducible bounded symmetric domain Ω of rank 2, where gD denotes the canonical Kähler–Einstein metric on any irreducible bounded symmetric domain D normalized so that minimal disks of D are of constant Gaussian curvature 2. In particular, results concerning the upper bound of the dimension of isometrically embedded Bn in Ω and the structure of the images of such holomorphic isometries are obtained.

In the second part, we study holomorphic isometries from (Bn ,gBn) to (Ω,gΩ) for any irreducible bounded symmetric domains Ω N of rank equal to 2 with 2N > N + 1, where N is an integer such that ι : XcN is the minimal embedding (i.e., the first canonical embedding) of the compact dual Hermitian symmetric space Xc of Ω. We completely classify images of all holomorphic isometries from (Bn ,gBn) to (Ω,gΩ) for 1 n n0(Ω), where n0(Ω) := 2N N > 1. In particular, for 1 n n0(Ω) 1 we prove that any holomorphic isometry from (Bn ,gBn) to (Ω,gΩ) extends to some holomorphic isometry from (Bn0(Ω) ,gBn 0(Ω)) to (Ω,gΩ).

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/pjm

We have not been able to recognize your IP address 34.231.247.139 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Bergman metrics, holomorphic isometric embeddings, bounded symmetric domains, Borel embedding, complex unit balls
Mathematical Subject Classification 2010
Primary: 32M15, 53C55, 53C42
Milestones
Received: 3 February 2017
Revised: 1 November 2017
Accepted: 5 February 2018
Published: 11 April 2018
Authors
Shan Tai Chan
Department of Mathematics
Syracuse University
Syracuse, NY
United States