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September 2011 Geometry of G2 orbits and isoparametric hypersurfaces
Reiko Miyaoka
Nagoya Math. J. 203: 175-189 (September 2011). DOI: 10.1215/00277630-1331899

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.

Citation

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Reiko Miyaoka. "Geometry of G2 orbits and isoparametric hypersurfaces." Nagoya Math. J. 203 175 - 189, September 2011. https://doi.org/10.1215/00277630-1331899

Information

Published: September 2011
First available in Project Euclid: 18 August 2011

zbMATH: 1231.53051
MathSciNet: MR2834253
Digital Object Identifier: 10.1215/00277630-1331899

Subjects:
Primary: 53C40
Secondary: 32L25, 53C30

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.203 • September 2011
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