On the Sign of the Curvature of a Contact Metric Manifold

David E. Blair
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David E. Blair: Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Mathematics, 2019, vol. 7, issue 10, 1-10

Abstract: In this expository article, we discuss the author’s conjecture that an associated metric for a given contact form on a contact manifold of dimension ≥5 must have some positive curvature. In dimension 3, the standard contact structure on the 3-torus admits a flat associated metric; we also discuss a local example, due to Krouglov, where there exists a neighborhood of negative curvature on a particular 3-dimensional contact metric manifold. In the last section, we review some results on contact metric manifolds with negative sectional curvature for sections containing the Reeb vector field.

Keywords: contact manifolds; associated metrics; curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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