We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to A-connection, we construct Weyl projective tensor In this way, obtain new conditions for manifold be projectively flat. At end of paper, define η-Einstein manifolds θ-th kind and prove that they coincide

Using symmetry arguments only, we show that every spacetime with mirror-symmetric spatial sections is necessarily conformally flat. The general form of the Ricci tensor of such spacetimes is also determined. 1. Introduction. It is well known that the curvature tensor of any four-dimensional differentiable manifold has only 20 algebraically independent components. Ten out of these 20 components ...

A Weyl solution describing two Schwarzschild black holes is considered. We focus on the Z2 invariant solution, with ADM mass MADM = 2MK , where MK is the Komar mass of each black hole. For this solution the set of fixed points of the discrete symmetry is a totally geodesic sub-manifold. The existence and radii of circular photon orbits in this sub-manifold are studied, as functions of the dista...

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kähler ; in the non-exact Einstein-Weyl case with a Bianchi metri...

For an arbitrary simple Lie algebra g and an arbitrary root of unity q, the closed subsets of the Weyl alcove of the quantum group Uq(g) are classified. Here a closed subset is a set such that if any two weights in the Weyl alcove are in the set, so is any weight in the Weyl alcove which corresponds to an irreducible summand of the tensor product of a pair of representations with highest weight...

We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRWmodels have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly correcti...

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kahler ; in the non-exact Einstein-Weyl case with a Bianchi metr...

We compute the number of linearly independent ways in which a tensor of Weyl type may act upon a given irreducible tensor-spinor bundle V over a Riemannian manifold. Together with the analogous but easier problem involving actions of tensors of Einstein type, this enumerates the possible curvature actions on V.