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

Beldjilali, Gherici; Belkhelfa, Mohamed

J. Geom. Symmetry Phys. 42, 1-13 (2016).

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

Keywords:

Kählerian structures; product manifolds; Sasakian structures