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In this paper, we classify all nonconstant smooth CR maps from a sphere Sn,1 ⊂ ℂ^n with n>3 to the Shilov boundary S_(p,q) ⊂ ℂ_(p×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 nonlinearmaps.
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참고문헌 (16)
참고문헌 신청
Alexander, H. / 1974 / Holomorphic mappings from the ball and polydisc / Math. Ann 209 : 249 ~ 256
Chern, S.S / 1974 / Real hypersurfaces in complex manifolds / Acta Math 133 : 219 ~ 271
Ebenfelt, P. / 2004 / Rigidity of CR-immersions into spheres / Comm. in Analysis and Geometry 12 (3) : 631 ~ 670
Faran V, J.J. / 1986 / On the linearity of proper maps between balls in the lower codimensional case / J. Differential Geom 24 : 15 ~ 17
Forstneri·c, F. / 1986 / Proper holomorphic maps between balls / Duke Math. J 53 : 427 ~ 440
Chern, S.S / 1974 / Real hypersurfaces in complex manifolds / Acta Math 133 : 219 ~ 271
Ebenfelt, P. / 2004 / Rigidity of CR-immersions into spheres / Comm. in Analysis and Geometry 12 (3) : 631 ~ 670
Faran V, J.J. / 1986 / On the linearity of proper maps between balls in the lower codimensional case / J. Differential Geom 24 : 15 ~ 17
Forstneri·c, F. / 1986 / Proper holomorphic maps between balls / Duke Math. J 53 : 427 ~ 440
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