Symplectic geometric flows

TL;DR

This paper introduces new symplectic geometric flows inspired by Type IIA flow and T-duality, including the Hitchin gradient flow and a novel dual Ricci flow, with potential applications in symplectic geometry and topology.

Contribution

It presents new symplectic flows, notably the Hitchin gradient flow and dual Ricci flow, expanding the toolkit for symplectic geometric analysis.

Findings

Introduction of the Hitchin gradient flow on symplectic manifolds

Definition of a new flow called the dual Ricci flow

Motivation from Type IIA flow and T-duality concepts

Abstract

Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in complex geometry. Examples include the Hitchin gradient flow on symplectic manifolds, and a new flow which is called the dual Ricci flow.