On the topology of metric f–K-contact manifolds

Abstract

We observe that the class of metric f -K-contact manifolds, which naturally contains that of K-contact manifolds, is closed under forming mapping tori of automorphisms of the structure. We show that the de Rham cohomology of compact metric f -K-contact manifolds naturally splits off an exterior algebra, and relate the closed leaves of the characteristic foliation to its basic cohomology.2010 Mathematics Subject Classification. Primary 53C25, 53C15, Secondary 53D10, 32V05.

Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

“…Is a compact weak f -Kcontact Einstein manifold an S-manifold? When a given weak f -K-contact manifold is a mapping torus (see [18]) of a manifold of lower dimension? When a weak f -contact manifold equipped with a Ricci-type soliton structure, carries a canonical (for example, with constant sectional curvature or Einstein-type) metric?…”

“…In the next theorem, we characterize weak f -K-contact manifolds among all weak f -contact manifolds by the following well known property of f -K-contact manifolds, see [4,18]:…”

“…An f -K-contact structure, i.e. an f -contact structure, whose characteristic vector fields are unit Killing vector fields, see [18], can be regarded as intermediate between a metric f -structure and S-structure (the Sasaki structure when s = 1). The influence of constant length Killing vector fields on the geometry of Riemannian manifolds has been studied by several authors from different points of view, e.g., [2,12].…”

Metric f-Contact Manifolds Satisfying the (κ, μ)-Nullity Condition

“…Moreover, S-structures are a natural generalization of Sasakian structures. However, unlike Sasakian manifolds, no S-structure can be realized on a simply connected compact manifold [7] (see also (Corollary 4.3,[8])). In [9], an example of an even dimensional principal toroidal bundle over a Kaehler manifold which does not carry any Sasakian structure is presented and an S-structure on the even dimensional manifold U(2) is constructed.…”

Metric $f$-contact manifolds satisfying the $(κ,μ)$-nullity condition

“…Moreover, S-structures are a natural generalization of Sasakian structures. However, unlike Sasakian manifolds, no S-structure can be realized on a simply connected compact manifold [8] (see also [14,Corollary 4.3]). In [10], an example of an even dimensional principal toroidal bundle over a Kaehler manifold which does not carry any Sasakian structure is presented and an S-structure on the even dimensional manifold U (2) is constructed.…”