• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ 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 $S_{n,1}$ and $S_{p,q}$ 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.