A Parabolic Flow of Pluriclosed Metrics

Generalized Kähler geometry and the pluriclosed flow

“…The purpose of this note is to show that the pluriclosed flow introduced in [16] preserves generalized Kähler geometry. This introductory section introduces the main results in a primarily mathematical context, while a physical discussion of the results appears in section 2.…”

“…It follows from Theorem 1.2 in [16] that with ω ± as initial metrics, we get solutions ω ± (t) of (1.2) on M × [0, T ± ). Let g ± (t) be the Hermitian metric on M whose Kähler form is ω ± (t).…”

“…In [16] the authors introduced a parabolic flow for pluriclosed metrics, referred to as pluriclosed flow. We also demonstrated in [17] that this flow, after certain gauge transformations, gives a class of solutions to the renormalization group flow of the nonlinear sigma model with B-field.…”

Product of generalized p-Kähler manifolds

“…A 1−Kähler manifold is simply a Kähler manifold, while 1−symplectic manifolds are also called hermitian symplectic ( [24]). In [9] pluriclosed (i.e.…”

“…In [9] pluriclosed (i.e. 1−pluriclosed) metrics are defined (see also [24]); a 1PL metric (manifold) is often called a strong Kähler metric (manifold) with torsion (SKT) (see among others [11]). Finally, 1WK forms are used, f.i., in [7], Theorem 1.2.…”