A spinorial energy functional: critical points and gradient flow

Abstract

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, ϕ) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor ϕ. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.

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References in corpus (6)

• The spinorial energy functional on surfaces
• A spinorial energy functional: critical points and gradient flow
• The Cauchy problems for Einstein metrics and parallel spinors
• Dirac eigenspinors for generic metrics
• Energy functionals and soliton equations for G_2-forms
• Ricci-flat deformations and special holonomy

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• Pin Groups in General Relativity
• The spinorial energy functional: solutions of the gradient flow on Berger spheres
• Stability of the Spinor Flow
• Blowup criteria for geometric flows on surfaces
• A gradient flow of Spin(7)-structures
• Construction of initial data sets for Lorentzian manifolds with lightlike parallel spinors
• An energy functional on the universal spinor bundle
• Spinor flows with flux, I: short-time existence and smoothing estimates
• Regularity estimates for the gradient flow of a spinorial energy functional