Generalized Goldberg Formula
Differential Geometry
2019-08-15 v3
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 -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 Kaehler 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.
Cite
@article{arxiv.1503.08740,
title = {Generalized Goldberg Formula},
author = {Antonio De Nicola and Ivan Yudin},
journal= {arXiv preprint arXiv:1503.08740},
year = {2019}
}
Comments
12 pages, accepted for publication in the Canadian Mathematical Bulletin