Kählerian Manifold on the Product of Two Trans-Sasakian Manifolds

Abstract

It's shown that for some changes of metrics and structural tensors, the product of two Trans-Sasakian manifolds is a K\"{a}hlerian manifold. This gives a new positive answer and more generally to Blair-Oubi$\tilde{n}$a's open question (see [7] and [17]). Concrete examples are given.                                                                                                            .......................................................................                                                                     

Keywords

• Trans-Sasakian manifolds
• K\"ahlerian manifolds
• product manifolds

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