Kählerian Structures and $\mathcal{D}$-Homothetic Bi-Warping

Abstract

We introduce the notion of $\mathcal{D}$-homothetic bi-warping and starting from a Sasakian manifold $M$, we construct a family of Kählerian structures on the product $\mathbb{R} \times M.$ After, we investigate conditions on the product of a cosymplectic or Kenmotsu manifold and the real line to be a family of conformal Kähler manifolds. We construct several examples.