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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.22 No.1

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SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.1, pp.35-56
https://doi.org/10.7468/jksmeb.2015.22.1.35
Kim, Sung-Yeon
Kim,, S. (2015). SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(1), 35-56, https://doi.org/10.7468/jksmeb.2015.22.1.35

Abstract

In this paper, we classify all nonconstant smooth CR maps from a sphere <TEX>$S_{n,1}{\subset}\mathbb{C}^n$</TEX> with n > 3 to the Shilov boundary <TEX>$S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$</TEX> of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of <TEX>$S_{n,1}$</TEX> and <TEX>$S_{p,q}$</TEX> or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

keywords
bonded symmetric domains, Shilov boundary, CR embedding, totally geodesic embedding, Whitney map

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