A dimensional restriction for a class of contact manifolds

Abstract

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.

Keywords

• almost contact metric structure
• contact manifold
• Chinea-Gonzalez classification
• 53D15
• 53D25
• 53C15
• 53D10