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On the Sign of the Curvature of a Contact Metric Manifold

Author

Listed:
  • David E. Blair

    (Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA)

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.

Suggested Citation

  • David E. Blair, 2019. "On the Sign of the Curvature of a Contact Metric Manifold," Mathematics, MDPI, vol. 7(10), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:892-:d:270185
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