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-Kähler 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 Kähler manifolds. We also discuss possible applications to Lagrangian submanifolds and calibrated geometry.

From Lagrangian to totally real geometry: coupled flows and calibrations

Tommaso Pacini
2020

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-Kähler 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 Kähler manifolds. We also discuss possible applications to Lagrangian submanifolds and calibrated geometry.
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Jason D. Lotay; Tommaso Pacini
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1742231
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