Holonomy and metric properties of foliations in higher codimension
Alexander P. Morgan
Abstract
Alexander P. Morgan
Abstract
It is well known that a codimension 1 foliation with finite holonomy on a compact manifold must have a bundle-like metric. A counterexample is presented to the higher codimension generalization of this theorem. However, a stronger holonomy restriction (expressed via the Bott connection) is shown to imply the existence of a bundle-like metric.
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It is well known that a codimension 1 foliation with finite holonomy on a compact manifold must have a bundle-like metric. A counterexample is presented to the higher codimension generalization of this theorem. However, a stronger holonomy restriction (expressed via the Bott connection) is shown to imply the existence of a bundle-like metric.
Key concepts: Holonomy, Codimension, Counterexample, Mathematics, Pure mathematics, Connection (principal bundle), Generalization, Metric (unit)