Evolve nondegenerate two forms

Abstract

We introduce geometric flows on a compact almost complex manifold, with the aim to flow a nondegenerate two form to a symplectic two form. We discuss mainly two flows, $d^{\ast }d$-flow and $d^{\ast }d$-Ricci flow. Among others, we prove the uniqueness and short time existence for smooth initial data. We also discuss the extension problem and a long time example on the warped product.

Comments are welcome

References in corpus (1)

• Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness