English

On Sasakian manifolds with special transverse holonomy

Differential Geometry 2012-12-05 v3

Abstract

We study compact Sasakian manifolds whose Tondeur connection has holonomy group either trivial or contained in Sp(n). We show that the first condition forces the manifold to be a compact quotient of the Heisenberg Lie group, while in the simply-connected case a Sasakian structure has the holonomy of the Tondeur connection contained in Sp(n) if and only if there exists a transverse hypercomplex structure. This latter result is the "Sasakian version" of a theorem of Verbitsky.

Keywords

Cite

@article{arxiv.1204.2839,
  title  = {On Sasakian manifolds with special transverse holonomy},
  author = {Luigi Vezzoni},
  journal= {arXiv preprint arXiv:1204.2839},
  year   = {2012}
}

Comments

The paper has been withdrawn, since the results therein have been included in the paper: On Riemannian Foliations with special transverse holonomy