Narrow Results

We discuss the role that non-Riemannian geometries might play in the formulation of modern higher-dimensional spacetime theories. Among the vast number of non-Riemannian geometries we consider the two simplest ones: Weyl geometry and Riemann-Cartan geometry. We approach the problem of classical confinement of particles in branes and show how this question may be investigated in the context of the two mentioned geometries. We show that there is a classical analogue of the confinement of fermions induced by a scalar field and the one that might be induced by a Weyl field. In similar fashion we show that the same role may be played by a torsion field.

We prove that a Ricci almost soliton on a Kenmotsu manifold of dimension $>3$ reduces to an expanding Ricci soliton satifying certain condition on the potential vector field or on the soliton function. Next, we show that any Ricci almost soliton on a Kenmotsu manifold is trivial (Einstein) if the soliton vector leaves the contact form $\eta$ invariant. Finally, we classify (locally) a Kenmotsu manifold admitting an almost Yamabe soliton. Some examples have been constructed of almost Yamabe solitons on different class of warped product spaces.