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On some 3-dimensional CR submanifolds in S 6

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 G 2. There exists a unique (up to G 2) 3-dimensional CR-submanifold which is obtained as an orbit of reducible representations of SU(2) on R 7. As orbits of the subgroup which corresponds to the irreducible representation of SU(2) on R 7, we obtained 2-parameter family of 3-dimensional CR-submanifolds. Next we give a generalization of the example which was obtained by K. Sekigawa.

Information

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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