Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds
Differential Geometry
2021-01-21 v1
Abstract
The very definition of an Einstein metric implies that all its geometry is encoded in the Weyl tensor. With this in mind, in this paper we derive higher-order Bochner type formulas for the Weyl tensor on a four dimensional Einstein manifold. In particular, we prove a second Bochner type formula which, formally, extends to the covariant derivative level the classical one for the Weyl tensor obtained by Derdzinski in 1983. As a consequence, we deduce some integral identities involving the Weyl tensor and its derivatives on a compact four dimensional Einstein manifold.
Keywords
Cite
@article{arxiv.1612.00627,
title = {Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds},
author = {Giovanni Catino and Paolo Mastrolia},
journal= {arXiv preprint arXiv:1612.00627},
year = {2021}
}