Generalized Killing spinors and Lagrangian graphs

Abstract

We study generalized Killing spinors on the standard sphere ${\mathbb{S}}^3$, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold $S^3\times S^3$ and to great circle flows on ${\mathbb{S}}^3$. Using our methods we generalize a well known result of Gluck and Gu concerning divergence-free geodesic vector fields on the sphere and we show that the space of Lagrangian submanifolds of $S^3\times S^3$ has at least three connected components.

11 pages

References in corpus (6)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• 3-Sasakian manifolds in dimension seven, their spinors and G_2 structures
• The Hermitian Laplace Operator on Nearly Kähler Manifolds
• The Cauchy problems for Einstein metrics and parallel spinors
• Generalized Killing spinors on Einstein manifolds
• Generalized Killing spinors on spheres

Cited by in corpus (9)

• Spinorial Representation of Submanifolds in Riemannian Space Forms
• On isotropic Lagrangian submanifolds in the homogeneous nearly Kähler ${\mathbb{S}}^3\times {\mathbb{S}}^3$
• Lagrangian submanifolds in the nearly kaehler $s^3\times s^3$
• Spinors of real type as polyforms and the generalized Killing equation
• Cauchy spinors on $3$-manifolds
• 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 ${\mathbb{S}}^3$
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures
• Lagrangian submanifolds of the nearly Kähler full flag manifold $F_{1,2}({\mathbb{C}}^3)$