Note on the conjecture of D.Blair in contact Riemannian geometry

Details Note on the conjecture of D.Blair in contact Riemannian geometry Note on the conjecture of D.Blair in contact Riemannian geometry

2011-07-30

arxiv.org/abs/1108.0082v1

Mathematics

Differential Geometry

7 pages, all comments are wellcome

Scientific paper

The conjecture of D.Blair says that there are no nonflat Riemannian metrics
of nonpositive curvature compatible 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. We also prove that a hyperbolic
metric on $\mathbb{R}^3$ cannot be compatible with any contact structure.

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