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

Volume 21, Number 2 (2018), 1 - 14

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

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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 K\"ahlerian structure on the product of two almost contact metric structures. It is shown that if one factor is $\beta$-Kenmotsu, the other is $\beta$-Kenmotsu or $\alpha$-Sasakian, and if one factor is cosymplectic, the other is $\alpha$-Sasakian, but the product of two $\alpha$-Sasakian is never K\"ahlerian. Several examples are discussed.