Reductions of minimal Lagrangian submanifolds with symmetries

Toru Kajigaya

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arXiv · 1710.05535

Reductions of minimal Lagrangian submanifolds with symmetries

Toru Kajigaya

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Abstract

Let $M$ be a Fano manifold equipped with a Kähler form $ω\in 2πc_1(M)$ 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 $L_0=L/K$ in a Kähler quotient $M_0$ 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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BibTeX RIS

Toru Kajigaya. 2017-10-26. Reductions of minimal Lagrangian submanifolds with symmetries. https://arxiv.org/abs/1710.05535

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