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Generalized Goldberg Formula

Published online by Cambridge University Press:  20 November 2018

Antonio De Nicola  and
Ivan Yudin
Antonio De Nicola
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal e-mail: [email protected] e-mail: [email protected]
Ivan Yudin
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal e-mail: [email protected] e-mail: [email protected]
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Abstract

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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.

Keywords

53C2553D35graded commutatorHodge codifferentialHodge Laplaciande Rham cohomologylocally conformal Kaehler manifoldquasi-Sasakian manifold
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 508 - 520
Copyright
Copyright © Canadian Mathematical Society 2016

References

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