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Generalized Goldberg Formula

  • Antonio De Nicola (a1) and Ivan Yudin (a1)


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.



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[8] Fujitani, T., Complex-valued differential forms on normal contact Riemannian manifolds. Tôhoku Math. J. (2) 18(1966), 349361.
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Generalized Goldberg Formula

  • Antonio De Nicola (a1) and Ivan Yudin (a1)


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