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arXiv · 2208.00421

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

Benjamin Aslan
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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.

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Benjamin Aslan. 2022-07-31. Special Lagrangians in nearly Kähler $\mathbb{CP}^3$. https://doi.org/10.1016/j.geomphys.2022.104713

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