Sasaki-like almost contact complex Riemannian manifolds

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold whose complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian manifold from a holomorphic complex Riemannian manifold is provided as an S1S1-solvable extension.