Structures and $\mathcal{D}$-isometric warping

Abstract

We introduce the notion of $\mathcal{D}$-isometric warping and prove some basic properties. We give an application to some questions of the characterization of certain geometric structures. Firstly, we construct a $1$-parameter family of K\"ahlerian structures from a single Sasakian structure with a concrete example. Secondly, we build a quaternionic K\"ahlerian structure from a $3$-Sasakian structures.