Nagoya Mathematical Journal

Geometry of G2 orbits and isoparametric hypersurfaces

Reiko Miyaoka

Full-text: Open access

Abstract

We characterize the adjoint G2 orbits in the Lie algebra g of G2 as fibered spaces over S6 with fibers given by the complex Cartan hypersurfaces. This combines the isoparametric hypersurfaces of case (g,m)=(6,2) with case (3,2). The fibrations on two singular orbits turn out to be diffeomorphic to the twistor fibrations of S6 and G2/SO(4). From the symplectic point of view, we show that there exists a 2-parameter family of Lagrangian submanifolds on every orbit.

Article information

Source
Nagoya Math. J., Volume 203 (2011), 175-189.

Dates
First available in Project Euclid: 18 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1313682316

Digital Object Identifier
doi:10.1215/00277630-1331899

Mathematical Reviews number (MathSciNet)
MR2834253

Zentralblatt MATH identifier
1231.53051

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 32L25: Twistor theory, double fibrations [See also 53C28]

Citation

Miyaoka, Reiko. Geometry of $G_{2}$ orbits and isoparametric hypersurfaces. Nagoya Math. J. 203 (2011), 175--189. doi:10.1215/00277630-1331899. https://projecteuclid.org/euclid.nmj/1313682316


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