Differential Geometry Working Seminar

Amanda Maria Petcu, University of Waterloo

Cohomogeneity one solitons of the hypersymplectic flow

Given a manifold X^4 x T^3 where X^4 is hypersymplectic, one can give a flow of hypersymplectic structures that evolve according to the equation dt(w) = d(Q d^*(Q^{-1} w)), where w is the triple that gives the hypersymplectic structure and Q is a 3x3 symmetric matrix that relates the symplectic forms w_i to one another. We will let X^4 be R^4 with a cohomogeneity one action and explain what it means to be a soliton for the hypersymplectic flow and examine a (potentially hyperkahler) metric that comes from this set-up.

MC 5479