From Lagrangian to totally real geometry: coupled flows and calibrations

Author: 

Lotay, J
Pacini, T

Publication Date: 

6 July 2020

Journal: 

Communications in Analysis and Geometry

Last Updated: 

2021-03-10T19:04:33.463+00:00

Issue: 

3

Volume: 

28

page: 

607-675

abstract: 

We show that the properties of Lagrangian mean curvature flow are a special
case of a more general phenomenon, concerning couplings between geometric flows
of the ambient space and of totally real submanifolds. Both flows are driven by
ambient Ricci curvature or, in the non-K\"ahler case, by its analogues. To this
end we explore the geometry of totally real submanifolds, defining (i) a new
geometric flow in terms of the ambient canonical bundle, (ii) a modified volume
functional which takes into account the totally real condition. We discuss
short-time existence for our flow and show it couples well with the
Streets-Tian symplectic curvature flow for almost K\"ahler manifolds. We also
discuss possible applications to Lagrangian submanifolds and calibrated
geometry.

Symplectic id: 

968682

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article