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

Vladimir Krouglov

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

Differential Geometry 2011-08-02 v1

Authors: Vladimir Krouglov

Abstract

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.

Keywords

contact Riemannian geometry Blair conjecture nonpositive curvature contact structure hyperbolic metric 3-manifold

Cite

@article{arxiv.1108.0082,
  title  = {Note on the conjecture of D.Blair in contact Riemannian geometry},
  author = {Vladimir Krouglov},
  journal= {arXiv preprint arXiv:1108.0082},
  year   = {2011}
}

Comments

7 pages, all comments are wellcome

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