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From Lagrangian to totally real geometry: coupled flows and calibrations

Lotay, JD; Pacini, T; (2020) From Lagrangian to totally real geometry: coupled flows and calibrations. Communications in Analysis and Geometry , 28 (3) pp. 607-675. 10.4310/CAG.2020.v28.n3.a5. Green open access

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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.

Type: Article
Title: From Lagrangian to totally real geometry: coupled flows and calibrations
Open access status: An open access version is available from UCL Discovery
DOI: 10.4310/CAG.2020.v28.n3.a5
Publisher version: https://doi.org/10.4310/CAG.2020.v28.n3.a5
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1429918
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