The Metrics G = agS + bgH + cgV on the Tangent Bundle of a Weyl Manifold

Let (M, [g]) be a Weyl manifold and TM be its tangent bundle equipped with Riemannian g−natural metrics which are linear combinations of Sasaki, horizontal and vertical lifts of the base metric with constant coefficients. The aim of this paper is to construct a Weyl structure on TM and to show that TM cannot be Einstein-Weyl even if (M, g) is fiat.

Sasaki metric on the tangent bundle of a Weyl manifold

Let (M, [g]) be a Weyl manifold of dimension m > 2. By using the Sasaki metric G induced by g, we construct a Weyl structure on TM. Then we prove that it is never Einstein-Weyl unless (M, g) is flat. The main theorem here extends to the Weyl context a result of Musso and Tricerri.

On quasi-Einstein Weyl manifolds

In this work, first, we define quasi-Einstein Weyl manifold which is one of the generalization of Einstein–Weyl manifold. Then, we prove its existence and construct an example. Moreover, we consider quasi-Einstein Weyl manifolds with semi-symmetric and Ricci-quarter symmetric connections. Finally, we examine conformal and generalized concircular mappings of quasi-Einstein Weyl manifolds and prove that quasi-Einstein Weyl manifolds are invariant under the generalized concircular mappings.

On the Classification of Almost Kenmotsu Manifolds of Dimension 3

This paper deals with the classification of a 3-dimensional almost Kenmotsu manifold satisfying certain geometric conditions. Moreover, by applying our main classification theorem, we obtain some suffcient conditions for an almost Kenmotsu manifold of dimension 3 to be an Einstein-Weyl manifold.