Differential Geometry Working Seminar | Faisal Romshoo | Torsion-free hypersymplectic structures

Faisal Romshoo (University of Waterloo)

Torsion-free hypersymplectic structures

We know that a torsion-free \(\mathrm{G}_2-\)structure determines a Riemannian metric with holotomy contained in \(\mathrm{G}_2\). However, a torsion-free hypersymplectic structure in dimension \($4$\) is not necessarily a hyperkähler structure. We will look at a counterexample and see under what conditions does a torsion-free hypersymplectic structure determine a hyperkähler structure.

MC 5417