Tohoku Mathematical Journal

A note on the conjecture of Blair in contact Riemannian geometry

Vladimir Krouglov

Full-text: Open access

Abstract

The conjecture of Blair says that there are no nonflat Riemannian metrics of nonpositive curvature associated with a contact structure. We prove this conjecture for a certain class of contact structures on closed 3-dimensional manifolds and construct a local counterexample.

Article information

Source
Tohoku Math. J. (2), Volume 64, Number 4 (2012), 561-567.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1356038978

Digital Object Identifier
doi:10.2748/tmj/1356038978

Mathematical Reviews number (MathSciNet)
MR3008238

Zentralblatt MATH identifier
1259.53074

Subjects
Primary: 53D10: Contact manifolds, general
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)

Keywords
Contact metric manifolds associated metrics

Citation

Krouglov, Vladimir. A note on the conjecture of Blair in contact Riemannian geometry. Tohoku Math. J. (2) 64 (2012), no. 4, 561--567. doi:10.2748/tmj/1356038978. https://projecteuclid.org/euclid.tmj/1356038978


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References

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