Cayley 4-form, comass, and triality isomorphisms

dc.creatorKatz, Mikhail G.
dc.creatorShnider, Steven
dc.date2008-01-01
dc.date2008-10-24
dc.date.accessioned2026-07-07T10:12:33Z
dc.date.available2026-07-07T10:12:33Z
dc.descriptionFollowing 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.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0801.0283
dc.identifierhttp://arxiv.org/abs/0801.0283
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172220
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subjectRepresentation Theory
dc.subject53C23; 17B25
dc.titleCayley 4-form, comass, and triality isomorphisms
dc.typetext

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