Special solutions to the Type IIA flow

Abstract

We consider the source-free Type IIA flow introduced by Fei-Phong-Picard-Zhang, and we study it in the case where the relevant geometric datum is a symplectic half-flat SU(3)-structure. We show the existence of ancient, immortal and eternal solutions to the flow, provided that the initial symplectic half-flat structure satisfies suitable properties. In particular, we prove that the solution starting at a symplectic half-flat structure with Hermitian Ricci tensor is ancient and evolves self-similarly by scaling the initial datum. These results apply to all known (locally) homogeneous spaces admitting invariant symplectic half-flat SU(3)-structures.

26 pages. v2: section 5 and appendix A added, section 6 reorganized

References in corpus (5)

• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• Geometric Partial Differential Equations from Unified String Theories
• $S^1$-invariant Laplacian flow
• Geometric Flows for the Type IIA String
• Bochner-Kodaira Formulas and the Type IIA Flow

Cited by in corpus (1)

• Symplectic geometric flows