Kählerian Structures on Generalized Doubly $\mathcal{D}$-Homothetic Bi-Warping

Abstract

In this paper we give a generalization of the doubly $\mathcal{D}$-homothetically warped metric introduced by Blair [4], and we study the construction of Kählerian structure on the product of two almost contact metric structures. It is shown that if one factor is $β$-Kenmotsu, the other is $β$-Kenmotsu or $α$-Sasakian, and if one factor is cosymplectic, the other is $α$-Sasakian, but the product of two $α$-Sasakian is never Kählerian. Several examples are discussed.