Seminar by Marco Freibert (University of Kiel)

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

2017.05.31 | Jane Jamshidi

Date Wed 07 Jun
Time 13:30 14:30
Location 1532 – 116 (Aud G1)

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.

AaDAG seminar