TY - JOUR
T1 - On a family of real hypersurfaces in a complex quadric
AU - Isaev, A. V.
PY - 2014/3
Y1 - 2014/3
N2 - We discuss a family Mtn, with n ≥ 2, t > 1, of real hypersurfaces in a complex affine n-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in Cn due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of Mtn in Cn for n = 3, 7. We show that Mt7 does not embed in C7 for every t and observe that Mt3 embeds in C3 for all t sufficiently close to 1. As a consequence of analyzing a map constructed by Ahern and Rudin, we also conjecture that Mt3 embeds in C3 for all 1
AB - We discuss a family Mtn, with n ≥ 2, t > 1, of real hypersurfaces in a complex affine n-dimensional quadric arising in connection with the classification of homogeneous compact simply-connected real-analytic hypersurfaces in Cn due to Morimoto and Nagano. To finalize their classification, one needs to resolve the problem of the embeddability of Mtn in Cn for n = 3, 7. We show that Mt7 does not embed in C7 for every t and observe that Mt3 embeds in C3 for all t sufficiently close to 1. As a consequence of analyzing a map constructed by Ahern and Rudin, we also conjecture that Mt3 embeds in C3 for all 1
KW - Global embeddability of CR-manifolds in complex space
UR - http://www.scopus.com/inward/record.url?scp=84895900847&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2013.10.004
DO - 10.1016/j.difgeo.2013.10.004
M3 - Article
SN - 0926-2245
VL - 33
SP - 259
EP - 266
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
ER -