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Sasakian structures a foliated approach

Wolak R. A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

72--82

Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena. Sasakian manifolds are odd dimensional counterparts of Kählerian manifolds to which they are closely related. The paper presents a foliated approach to Sasakian manifolds on which the author gave several lectures. The paper concentrates on cohomological properties of Sasakian manifolds and of transversely holomorphic and Kählerian foliations. These properties permit to formulate obstructions to the existence of Sasakian structures on compact manifolds.

A dimensional restriction for a class of contact manifolds

Loiudice E.

Demonstratio Mathematica

2017

Vol. 50, nr 1

231--238

In this work we consider a class of contact manifolds (M, η) with an associated almost contact metric structure (φ, ξ, η, g). This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class C9 ⊕ C10 defined by Chinea and Gonzalez. All manifolds in the class considered turn out to have dimension 4n + 1. Under the assumption that the sectional curvature of the horizontal 2-planes is constant at one point, we obtain that these manifolds must have dimension 5.