Reductions of minimal Lagrangian submanifolds with symmetries

2017/10/16 by Kajigaya, Toru
#53C42 #53D12 (Primary) #53D20 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.05535

Abstract

Let M be a Fano manifold equipped with a Kähler form ω∈ 2πc₁(M) and K a connected compact Lie group acting on M as holomorphic isometries. In this paper, we show the minimality of a K-invariant Lagrangian submanifold L in M w.r.t. a globally conformal Kähler metric is equivalent to the minimality of the reduced Lagrangian submanifold L₀=L/K in a Kähler quotient M₀ w.r.t. the Hsiang-Lawson metric. Furthermore, we give some examples of Kähler reductions by using a circle action obtained from a cohomogenenity one action on a Kähler-Einstein manifold of positive Ricci curvature. Applying these results, we obtain several examples of minimal Lagrangian submanifolds via reductions.

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