Nagoya Mathematical Journal

On some 3-dimensional CR submanifolds in $S\sp 6$

Hideya Hashimoto and Katsuya Mashimo

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Abstract

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 ${\bf R}^7$. As orbits of the subgroup which corresponds to the irreducible representation of $SU(2)$ on ${\bf R}^7$, we obtained 2-parameter family of 3-dimensional CR-submanifolds. Next we give a generalization of the example which was obtained by K. Sekigawa.

Article information

Source
Nagoya Math. J., Volume 156 (1999), 171-185.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631305

Mathematical Reviews number (MathSciNet)
MR1727899

Zentralblatt MATH identifier
0957.53023

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citation

Hashimoto, Hideya; Mashimo, Katsuya. On some 3-dimensional CR submanifolds in $S\sp 6$. Nagoya Math. J. 156 (1999), 171--185. https://projecteuclid.org/euclid.nmj/1114631305


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