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Annals of Global Analysis and Geometry

, Volume 53, Issue 3, pp 311–329 | Cite as

The spectral sequence of the canonical foliation of a Vaisman manifold

  • Liviu Ornea
  • Vladimir Slesar
Article
  • 70 Downloads

Abstract

In this paper we investigate the spectral sequence associated with a Riemannian foliation which arises naturally on a Vaisman manifold. Using the Betti numbers of the underlying manifold we establish a lower bound for the dimension of some terms of this cohomological object. This way we obtain cohomological obstructions for two-dimensional foliations to be induced from a Vaisman structure. We show that if the foliation is quasi-regular the lower bound is realized. In the final part of the paper we discuss two examples.

Keywords

Locally conformally Kähler Canonical foliation Vaisman manifold Spectral sequence 

Mathematics Subject Classification

53C55 53C12 

Notes

Acknowledgements

We acknowledge useful discussions with J. Álvarez López concerning the geometrical meaning of the spectral term \(E_2^{0,1}\). We also thank the referee for very carefully reading a first version of the paper and for his most useful suggestions.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Research Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  2. 2.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  3. 3.Department of Mathematical Methods and ModelsUniversity Politehnica of BucharestBucharestRomania

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