Mathematisches Seminar

Dr. Sergey Grigorian, University Texas Rio Grande Valley: "G2-structures and octonion bundles"

18.07.2017 von 14:15 bis 15:45

LMS 4 - Raum 526 - Übungsraum

Abstract:

We use a G2-structure on a 7-dimensional Riemannian manifold to define an octonion bundle with a fiberwise non-associative product. We then define a metric-compatible octonionic covariant derivative on this bundle that is also compatible with the octonion product. The torsion of the G2-structure is then shown to be an octonionic connection for this covariant derivative with curvature given by the component of the Riemann curvature that lies in the 7-dimensional representation of G2. The choice of a particular G2-structure within the same metric class is then interpreted as a choice of gauge and we show that under a change of this gauge, the torsion transforms as an octonion-valued connection 1-form. Finally, we also explore an energy functional for octonion sections, the critical points of which are shown to correspond to an octonionic analog of the Coulomb gauge.

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