Special Lagrangians in nearly Kähler ${\mathbb{CP}}^3$

Abstract

This article explores special Lagrangian submanifolds in ${\mathbb{CP}}^3$, viewed as a nearly Kähler manifold, from two different perspectives. Intrinsically, using a moving frame set-up, and extrinsically, using $\mathrm{SU}(2)$ moment-type maps. We describe new homogeneous examples, from both perspectives, and classify totally geodesic special Lagrangian submanifolds. We show that every special Lagrangian in ${\mathbb{CP}}^3$, or the flag manifold ${\mathbb{F}}_{1,2}({\mathbb{C}}^3)$ admitting a symmetry of an $\mathrm{SU}(2)$ subgroup of nearly Kähler automorphisms is automatically homogeneous.

21 pages, 1 table

Cited by in corpus (1)

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