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Geometry of G2 orbits and isoparametric hypersurfaces

Published online by Cambridge University Press:  11 January 2016

Reiko Miyaoka
Reiko Miyaoka*
Affiliation:
Mathematical Institute, Graduate School of Sciences, Tohoku University, Aoba-ku, Sendai 980-8578Japanr-miyaok@math.tohoku.ac.jp
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Abstract

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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.

Keywords

53C4053C3032L25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 203 , September 2011 , pp. 175 - 189
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

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