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arXiv · 1404.4227

From Lagrangian to totally real geometry: coupled flows and calibrations

Jason D. Lotay·Tommaso Pacini
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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.

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Jason D. Lotay, Tommaso Pacini. 2014-04-16. From Lagrangian to totally real geometry: coupled flows and calibrations. https://arxiv.org/abs/1404.4227

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