Data di Pubblicazione:
2020
Citazione:
Bochner-type formulas for the Weyl tensor on four-dimensional Einstein manifolds / G. Catino, P. Mastrolia. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - 2020:12(2020 Jun), pp. 3794-3823. [10.1093/imrn/rny127]
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 2nd Bochner-type formula that, 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.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
G. Catino, P. Mastrolia
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