Curvature of C 5 ⊕ C 12 -Manifolds

The Chinea–Gonzalez class C5⊕C12 consists of the almost contact metric manifolds that are locally described as double-twisted product manifolds I×(λ1,λ2)M^, I⊂R being an open interval, M^ a Kähler manifold and λ1,λ2 smooth positive functions. In this article, we investigate the behavior of the curvature of C5⊕C12-manifolds. Particular attention to the N(k)-nullity condition is given and some local classification theorems in dimension 2n+1≥5 are stated. This allows us to classify C5⊕C12-manifolds that are generalized Sasakian space forms. In addition, we provide explicit examples of these spaces.