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SU(4)-holonomy via the left-invariant Hitchin and hypo flow

Marco Freibert
(University of Kiel)
AaDAG seminar
Wednesday, 7 June, 2017, at 13:30-14:30, in Aud. G1 (1532-116)
Abstract:
The Hitchin flow in seven dimension starts with a real-analytic cocalibrated G2-structure and produces 8d Riemannian manifolds with holonomy in the exceptional holonomy group Spin(7).
Now the irreducible holonomy groups Sp(2) and SU(4) are subgroups of Spin(7) and so may also be obtained by the Hitchin flow. E.g. one gets holonomy in SU(4) if the initial cocalibrated G2-structure is induced by a hypo SU(3)-structure as then the Hitchin flow is induced by the hypo flow.
For both, the Hitchin and the hypo flow we study, in a left-invariant context on Lie groups, conditions on the initial value which ensure that the outcoming 8d Riemannian manifold has holonomy in or equal to SU(4) or not equal to Sp(2).
Moreover, we provide many explict examples of SU(4)-holonomy metrics obtained by the "diagonal" Hitchin flow on almost Abelian Lie algebras.
Organised by: QGM
Contact person: Andrew Swann