1976Proceedings of the American Mathematical SocietyRequires access

Holonomy and metric properties of foliations in higher codimension

Alexander P. Morgan

Open publisher page 5 citations

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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What this paper is about

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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Available 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.

Key concepts: Holonomy, Codimension, Counterexample, Mathematics, Pure mathematics, Connection (principal bundle), Generalization, Metric (unit)

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