Calculus of Variations and Geometric Measure Theory
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G. Catino - P. Mastrolia

Bochner type formulas for the Weyl tensor on four dimensional Einstein manifolds

created by catino on 02 Dec 2016
modified on 18 May 2018


Accepted Paper

Inserted: 2 dec 2016
Last Updated: 18 may 2018

Journal: Int. Math. Res. Not.
Year: 2018


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 new integral identities involving the Weyl tensor and its derivatives on a compact four dimensional Einstein manifold and we derive a new rigidity result.


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