CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Generalized Goldberg Formula

  Published:2016-02-12
 Printed: Sep 2016
  • Antonio De Nicola,
    CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
  • Ivan Yudin,
    CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Format:   LaTeX   MathJax   PDF  

Abstract

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 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 CDGA to the full de Rham algebra.
Keywords: graded commutator, Hodge codifferential, Hodge laplacian, de Rham cohomology, locally conformal Kaehler manifold, quasi-Sasakian manifold graded commutator, Hodge codifferential, Hodge laplacian, de Rham cohomology, locally conformal Kaehler manifold, quasi-Sasakian manifold
MSC Classifications: 53C25, 53D35 show english descriptions Special Riemannian manifolds (Einstein, Sasakian, etc.)
Global theory of symplectic and contact manifolds [See also 57Rxx]
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D35 - Global theory of symplectic and contact manifolds [See also 57Rxx]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/