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2 results

  • Generalized Goldberg Formula

  • Antonio De Nicola, Ivan Yudin
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 3 / 01 September 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 508-520
    Print publication:
    01 September 2016
    • Article
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  • 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.