Curvature of $C_5oplus C_{12}$-manifolds

The Chinea–Gonzalez class C5⊕ C12 consists of the almost contact metric manifolds that are locally described as double-twisted product manifolds $I imes_{lambda_1,lambda_2)}M$, I 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 2 n+ 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.