Tohoku Mathematical Journal
2012
December
SECOND SERIES VOL. 64, NO. 4

Tohoku Math. J.
64 (2012), 561-567

Title A NOTE ON THE CONJECTURE OF BLAIR IN CONTACT RIEMANNIAN GEOMETRY

Author Vladimir Krouglov

(Received August 18, 2011, revised February 27, 2012)
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.

2000 Mathematics Subject Classification. Primary 53D10; Secondary 53C25.
Key words and phrases. Contact metric manifolds, associated metrics.

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