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

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Inserted: 2 dec 2016
Last Updated: 2 dec 2016

Year: 2016

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.


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