Cayley 4-form, comass, and triality isomorphisms

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Following an idea of Dadok, Harvey and Lawson, we apply the triality property of SO(8) to study the comass of certain self-dual 4-forms on R^8. In particular, we prove that the Cayley 4-form has comass 1 and that any self-dual 4-form realizing the maximal Wirtinger ratio is SO(8)-conjugate to the Cayley 4-form. We also use triality to prove that the stabilizer in SO(8) of the Cayley form is Spin(7). The results have applications in systolic geometry, calibrated geometry, and Spin(7) manifolds.
20 pages

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Differential Geometry, Metric Geometry, Representation Theory, 53C23; 17B25

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http://salesiana.dossiersoluciones.com/handle/123456789/172220

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.0283
 http://arxiv.org/abs/0801.0283

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arXiv