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On some 3-dimensional CR submanifolds in S6

Published online by Cambridge University Press:  22 January 2016

Hideya Hashimoto  and
Katsuya Mashimo
Hideya Hashimoto
Affiliation:
Nippon Institute of Technology, 4-1, Gakuendai, Miyashiro, Minami-Saitama Gun, Saitama 345-8501, Japan, hideya@nit.ac.jp
Katsuya Mashimo
Affiliation:
Department of Mathematics, Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183-0054, Japan, mashimo@cc.tuat.ac.jp
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Abstract

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We give two types of 3-dimensional CR-submanifolds of the 6-dimensional sphere. First we study whether there exists a 3-dimensinal CR-submanifold which is obtained as an orbit of a 3-dimensional simple Lie subgroup of G2. There exists a unique (up to G2) 3-dimensional CR-submanifold which is obtained as an orbit of reducible representations of SU(2) on R7. As orbits of the subgroup which corresponds to the irreducible representation of SU(2) on R7, we obtained 2-parameter family of 3-dimensional CR-submanifolds. Next we give a generalization of the example which was obtained by K. Sekigawa.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 156 , 1999 , pp. 171 - 185
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

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