Reduced holonomy and Hodge theory

Gil R. Cavalcanti

Reduced holonomy and Hodge theory

Differential Geometry 2013-09-10 v2

Authors: Gil R. Cavalcanti

Abstract

We develop Hodge theory for a Riemannian manifold $(M,g)$ with a background closed 3-form, H. Precisely, we prove that if the metric connections with torsion $\pm H$ have holonomy groups $G_\pm$ , then the $d^H$ -Laplacian preserves the irreducible representations of the Lie algebras of the holonomy groups on the space of forms.

Keywords

hodge theory holonomy lie groups

Cite

@article{arxiv.1208.3558,
  title  = {Reduced holonomy and Hodge theory},
  author = {Gil R. Cavalcanti},
  journal= {arXiv preprint arXiv:1208.3558},
  year   = {2013}
}

Comments

This paper was incorporated into arxiv:1203.0493v4

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