  A Sasaki-like almost contact complex Riemannian manifold is defined as an
almost contact complex Riemannian manifold which 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 presented
and called an $S^1$-solvable extension.
