Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow

2024/09/19 by Yannick Sire, Sire, Yannick, Tian Xu +1
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2409.12430

Abstract

We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local well-posedness of smooth solutions. The present contribution is the first installment of more general program on the Einstein-Dirac problem.

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