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June, 2001 A Construction of New Families of Minimal Lagrangian Submanifolds via Torus Actions
Edward Goldstein
J. Differential Geom. 58(2): 233-261 (June, 2001). DOI: 10.4310/jdg/1090348326

Abstract

In this paper we investigate connections between minimal Lagrangian submanifolds and holomorphic vector fields in Kähler manifolds. Our main result is: Let M2n (n ≥ 2) be a Kähler-Einstein manifold with positive scalar curvature with an effective, structure-preserving action by an n-torus Tn. Then precisely one regular orbit L of the Tn-action is a minimal Lagrangian submanifold of M. Moreover there is an (n − 1)-torus Tn−1Tn and a sequence of non-flat immersed minimal Lagrangian tori Lk in M such that all Lk are invariant under Tn−1 and Lk locally converge to L (in particular the supremum of the sectional curvatures of Lk and the distance between L and Lk go to 0 as k ↦ ∞). This result is new even for M = ℂPn for n ≥ 3.

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Edward Goldstein. "A Construction of New Families of Minimal Lagrangian Submanifolds via Torus Actions." J. Differential Geom. 58 (2) 233 - 261, June, 2001. https://doi.org/10.4310/jdg/1090348326

Information

Published: June, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1050.53066
MathSciNet: MR1913943
Digital Object Identifier: 10.4310/jdg/1090348326

Rights: Copyright © 2001 Lehigh University

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Vol.58 • No. 2 • June, 2001
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