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Open AccessFeature PaperArticle

On the Sign of the Curvature of a Contact Metric Manifold

Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Mathematics 2019, 7(10), 892; https://doi.org/10.3390/math7100892
Received: 24 August 2019 / Revised: 18 September 2019 / Accepted: 18 September 2019 / Published: 24 September 2019
(This article belongs to the Special Issue Complex and Contact Manifolds)
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. View Full-Text
Keywords: contact manifolds; associated metrics; curvature contact manifolds; associated metrics; curvature
MDPI and ACS Style

Blair, D.E. On the Sign of the Curvature of a Contact Metric Manifold. Mathematics 2019, 7, 892.

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