Geodesic
Generalized Goldberg Formula
Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 508-520

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed $p$ -form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel $\text{I}$ . Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kähler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a $\text{CDGA}$ to the full de Rham algebra.
DOI : 10.4153/CMB-2016-007-4
Mots-clés : 53C25, 53D35, graded commutator, Hodge codifferential, Hodge Laplacian, de Rham cohomology, locally conformal Kaehler manifold, quasi-Sasakian manifold 
Nicola, Antonio De; Yudin, Ivan. Generalized Goldberg Formula. Canadian mathematical bulletin, Tome 59 (2016) no. 3, pp. 508-520. doi: 10.4153/CMB-2016-007-4
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