Reduced holonomy and Hodge theory

Gil R. Cavalcanti

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arXiv · 1208.3558

Reduced holonomy and Hodge theory

Gil R. Cavalcanti

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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.

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BibTeX RIS

Gil R. Cavalcanti. 2012-08-17. Reduced holonomy and Hodge theory. https://arxiv.org/abs/1208.3558

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