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arXiv · 2409.12430

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

Yannick Sire·Tian Xu
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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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Yannick Sire, Tian Xu. 2024-09-19. Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow. https://arxiv.org/abs/2409.12430

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