Generalized Goldberg Formula

Canadian mathematical bulletin

Ivan Yudin¹  Antonio De Nicola¹ 

[1] CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal

关键词: graded commutator;    Hodge codifferential;    Hodge laplacian;    de Rham cohomology;    locally conformal Kaehler manifold;    quasi-Sasakian manifold;   

DOI  :  10.4153/CMB-2016-007-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we prove a useful formula for the graded commutatorof the Hodgecodifferential with the left wedge multiplication by a fixed$p$-form acting onthe de Rham algebra of a Riemannian manifold. Our formula generalizesa formulastated by Samuel I. Goldberg for the case of 1-forms. As firstexamples ofapplication we obtain new identities on locally conformally Kählermanifoldsand quasi-Sasakian manifolds. Moreover, we prove that under suitableconditionsa certain subalgebra of differential forms in a compact manifoldis quasi-isomorphic as a CDGA to the full de Rham algebra.

【 授权许可】

Unknown