Intrinsically harmonic forms and characterization of flat circle bundles
Elizeu Fran\c{c}a, Francesco Mercuri
TL;DR
This paper provides a criterion for determining when a principal circle bundle is flat by linking flatness to the intrinsic harmonicity of an associated natural form.
Contribution
It introduces a new criterion connecting flatness of circle bundles with the intrinsic harmonicity of a specific form, offering a novel characterization.
Findings
Flatness is equivalent to the intrinsic harmonicity of a natural form.
Provides a new geometric criterion for flat circle bundles.
Establishes a link between bundle flatness and harmonic forms.
Abstract
We establish a criterion for the flatness of a principal circle bundle in terms of the intrinsically harmonic form problem. It states that the flatness is equivalent to the intrinsic harmonicity of a certain natural associated form.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology