Minimal Lagrangian tori in Kahler Einstein manifolds

2000/07/22 by Edward Goldstein, Goldstein, Edward
Earth and Planetary Sciences · Mathematics · #53XX #Differential Geometry (math.DG) #FOS: Mathematics #Geology and Paleoclimatology Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53XX

paper · pdf · doi:10.48550/arxiv.math/0007135

15 pages

arxiv created 2000/07/22 · openalex publication_date 2000/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we use structure preserving torus actions on Kahler-Einstein manifolds to construct minimal Lagrangian submanifolds. Our main result is: Let N²n be a Kahler-Einstein manifold with positive scalar curvature with an effective Tⁿ-action. Then precisely one regular orbit L of the T-action is a minimal Lagrangian submanifold of N. Moreover there is an (n-1)-torus Tⁿ-1 in Tⁿ and a sequence of non-flat immersed minimal Lagrangian tori L_k in N, invariant under Tⁿ-1 s.t. L_k locally converge to L (in particular the supremum of the sectional curvatures of L_k and the distance between L_k and L go to 0 as k goes to infinity.

Citations

• Calibrated geometries

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