## Kählerian structures and $$\mathcal D$$-homothetic bi-warping.(English)Zbl 1365.53029

Summary: 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.

### MSC:

 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53B35 Local differential geometry of Hermitian and Kählerian structures 53D25 Geodesic flows in symplectic geometry and contact geometry
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