New applications of the Ahlfors Laplacian
Differential Geometry
2023-02-07 v1
Abstract
In this article, we consider an orthogonal decomposition of the traceless part of the Ricci tensor of a compact Riemannian manifold and study its application to the geometry of compact almost Ricci solitons. In addition, we consider an orthogonal expansion of the traceless part of the second fundamental form of a compact spacelike hypersurface in a Lorentzian manifold and study its application to the problem of constructing solutions of general relativistic constraint equations in vacuum. In these two cases, we use the well-known Ahlfors Laplacian.
Keywords
Cite
@article{arxiv.2302.02799,
title = {New applications of the Ahlfors Laplacian},
author = {Sergey E. Stepanov and Josef Mikes and Irina I. Tsyganok},
journal= {arXiv preprint arXiv:2302.02799},
year = {2023}
}