Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow
Analysis of PDEs
2024-09-20 v1 Differential Geometry
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.
Cite
@article{arxiv.2409.12430,
title = {Conformal deformation of a Riemannian metric via an Einstein-Dirac parabolic flow},
author = {Yannick Sire and Tian Xu},
journal= {arXiv preprint arXiv:2409.12430},
year = {2024}
}