In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantity H, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Num...

Construction of an infinite dimensional differentiable manifold R∞ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P ∗ p M [[~]], ◦) and a Weyl algebra bundle (P∗M[[~]], ◦) are presented. Continuity of the ◦-product in the Tichonov topology is proved. Construction of the ∗-product of the Fedosov type in terms of theory of connectio...

In this paper, we evaluate energy and momentum density distributions for the Weyl metric by using the well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and Möller. The metric under consideration is the static axisymmetric vacuum solution to the Einstein field equations and one of the field equations represents the Laplace equation. Curzon metric is the special case of this spacet...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

We show that a large class of non–metric, non–symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS–structures on certain generalized flag manifolds.

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional basis space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G : • ...

We show that a large class of non–metric, non–symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS–structures on certain generalized flag manifolds.