Kählerian Structures and D-Homothetic Bi-Warping

Abstract

We introduce the notion of D-homothetic bi-warping and starting from a Sasakian manifold M , we construct a family of Kählerian structures on the product R × 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.

Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds

“…For this construction, we rely on our example in [2]. We denote the Cartesian coordinates in a 3-dimensional Euclidean space R 3 by (x, y, z) and define a symmetric tensor field g by…”

Almost contact metric and metallic Riemannian structures

“…First, note that for all i 2 f1; 2g we have i = i ; and using (1) and 17 Proof. Since the proof of the following proposition is obvious, we don't give the proof of it.…”

Generalized Kählerian manifolds and transformation of generalized contact structures

“…Recently, Beldjilali and Belkhelfa introduced a generalization of D-homothetic warped metric onM = M × M as follows [3]:…”

“…Results in our paper can be divided in two parts. In the first part, we construct generalized Kähler structures starting from classical odd-dimensional almost contact metric manifolds or even-dimensional almost Kählerian manifolds and using the D-homothetic bi-warping construction (see [3,6]). In the second part, we extend the D-homothetic transformation construction to generalized Riemannian manifolds.…”

“…In the second part, we extend the D-homothetic transformation construction to generalized Riemannian manifolds. The D-homothetic bi-warping [3,6] is a construction in classical Riemannian manifolds generalizing the warped product and defined as follows. Let (M 1 , g 1 ) be a Riemannian manifold together with two smooth functions f and h on M 1 …”