On Sasakian manifolds with special transverse holonomy

Luigi Vezzoni

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arXiv · 1204.2839

On Sasakian manifolds with special transverse holonomy

Luigi Vezzoni

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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.

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Luigi Vezzoni. 2012-04-12. On Sasakian manifolds with special transverse holonomy. https://arxiv.org/abs/1204.2839

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