We present a recent result about the Riemannian metric structure of the tangent manifold TM, the total space of the tangent bundle T M → M of any given Riemannian manifold M. We recall how such space is endowed with a metric, due to S. Sasaki, and which are its main properties. Following this, we show the construction of a fully original Hermitian structure, called ciconia, which leads to interesting Kähler-Einstein and, in particular, non-compact Calabi-Yau manifolds.