Differential Geometry Working Seminar

Wednesday, March 19, 2025 3:30 pm - 5:00 pm EDT (GMT -04:00)

Amanda Maria Petcu, University of Waterloo

A hypersymplectic structure on R^4 with an SO(4) action

Given a hypersymplectic manifold X^4, one can give a flow of hypersymplectic structures that evolve according to the equation

d_t w = d(Q d^*(Q^{-1} w), where w is the triple that gives the hypersymplectic structure and Q is a 3x3 symmetric matrix. In this talk we let X^4 be R^4 with an SO(4) action  The flow of the hypersymplectic triple then descends to a single flow of a function h. We will examine this flow, as well as solitons of the hypersymplectic flow in this set up. Furthermore, the triple w gives rise to a Riemannian metric g . We will conclude with a discussion about the Riemann and Ricci curvature tensors that are derived from this metric.

MC 5479