A non-Sasakian Lefschetz \(K\)-contact manifold of Tievsky type (Q2827381)
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scientific article; zbMATH DE number 6640954
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A non-Sasakian Lefschetz \(K\)-contact manifold of Tievsky type |
scientific article; zbMATH DE number 6640954 |
Statements
19 October 2016
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non-Sasakian Lefschetz \(K\)-contact manifold
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Tievsky type
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A non-Sasakian Lefschetz \(K\)-contact manifold of Tievsky type (English)
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In [Analogues of Kähler geometry on Sasakian manifolds. Cambridge, MA: Massachusetts Institute of Technology (Ph.D. Thesis) (2008)], \textit{A. M. Tievsky} proved that in order for a compact contact manifold \(M\) to admit a compatible Sasakian structure, its de Rham algebra has to be quasi-isomorphic as CGDA to an elementary Hirsch extension of the basic cohomology algebra with respect to the foliation induced by the Reeb vector field. Hence a compact contact manifold admitting the model \((\mathcal{T}(M), d)\) is called \textit{of Tievsky type}. The present paper introduces a family of five-dimensional compact completely solvable K-contact formal manifolds of Tievsky type with no Sasakian structure. Two descriptions of this family are provided.
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