Ruled Lagrangian Submanifolds of the 6-Sphere

Abstract

This article sets out to serve a dual purpose. On the one hand, we give an explicit description of the Lagrangian submanifolds of the nearly Kaehler 6-sphere which are ruled by circles of constant radius using Weierstrass formulae. On the other, we recognise all previous known examples of these Lagrangians as being ruled by such circles. Therefore, we describe all families of Lagrangians in the 6-sphere whose second fundamental form satisfies natural pointwise conditions: so-called second order families.

46 pages, v2: minor corrections, version to appear in Trans. Amer. Math. Soc

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Cited by in corpus (11)

• Associative Submanifolds of the 7-Sphere
• Deformation Theory of Asymptotically Conical Coassociative 4-folds
• The heterotic ${\mathrm{G}}_2$ system on contact Calabi--Yau $7$-manifolds
• Special Lagrangians in nearly Kähler ${\mathbb{CP}}^3$
• On isotropic Lagrangian submanifolds in the homogeneous nearly Kähler ${\mathbb{S}}^3\times {\mathbb{S}}^3$
• Lagrangian submanifolds in the nearly kaehler $s^3\times s^3$
• Desingularization of Coassociative 4-folds with Conical Singularities: Obstructions and Applications
• Lagrangian warped product immersions in ${\mathbb{S}}^6$
• Lagrangian Submanifolds with Constant Angle Functions of the nearly Kähler ${\mathbb{S}}^3\times {\mathbb{S}}^3$
• Lagrangian submanifolds of the nearly Kähler ${\mathbb{S}}^3\times {\mathbb{S}}^3$ from minimal surfaces in ${\mathbb{S}}^3$
• Lagrangian submanifolds of the nearly Kähler full flag manifold $F_{1,2}({\mathbb{C}}^3)$