  In this paper we provide an explicit description of normal almost contact
structures obtained from Cartan-Ehresmann connections (gauge fields) on
principal $S^{1}$-bundles over complex flag manifolds. The main feature of our
approach is to employ elements of representation theory of complex simple Lie
algebras in order to describe and classify these structures. We use these
normal almost contact structures to explicitly describe a huge class of compact
Hermitian non-K\"{a}hler manifolds obtained from products of principal
$S^{1}$-bundles over complex flag manifolds. Moreover, we obtain from our
description several concrete examples of 1-parametric families of complex
structures on products of principal $S^{1}$-bundles over flag manifolds, these
concrete examples generalize the Calabi-Eckmann manifolds. Further, as an
application of our main results in the setting of KT structures on toric
bundles over flag manifolds, we classify a huge class of explicit examples of
Calabi-Yau structures with torsion (CYT) on certain Vaisman manifolds
(generalized Hopf manifolds). Also as an application of our main results, we
provide several new concrete examples of astheno-K\"{a}hler structures on
products of compact homogeneous Sasaki manifolds.
