SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics Education, Kangwon National University)

Kim, Sung-Yeon. (2015). SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS. 한국수학교육학회지시리즈B:순수및응용수학, 22(1), 35-56, https://doi.org/10.7468/jksmeb.2015.22.1.35

복사

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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논문 상세

Vol.22 No.1

SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS

SPHERES IN THE SHILOV BOUNDARIES OF BOUNDED SYMMETRIC DOMAINS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학