On Sasakian manifolds with special transverse holonomy

Details On Sasakian manifolds with special transverse holonomy On Sasakian manifolds with special transverse holonomy

2012-04-12

arxiv.org/abs/1204.2839v2

Mathematics

Differential Geometry

11 pages. Section 2.2 modified

Scientific paper

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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