In the present paper, we have studied some properties of a semi-symmetric non-metric connection in HSU-unified structure manifold and HSU-Kahler manifold. Some new results on such manifolds been obtained.

The aim of this paper is to characterize a Riemannian 3-manifold M3 equipped with semi-symmetric metric ξ-connection ∇˜ ρ-Einstein and gradient solitons. existence soliton in an admitting ensured by constructing non-trivial example, hence some our results are verified. By using standard tensorial technique, we prove that the scalar curvature (M3,∇˜) satisfies Poisson equation ΔR=4(2−σ−6ρ)ρ.

Projective connections first appeared in Cartan’s papers in the 1920’s. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant quantisation. We recall the notion of projective connection and describe its relation with the algebra of densities on a manifold. In particular, we construct a Lapl...

Using the non-symmetric-connection approach proposed by Osborn, we demonstrate that, for a bosonic string in a specially chosen plane-fronted gravitational wave and an axion background, the conformal anomaly vanishes at the two-loop level. Under some conditions, the anomaly vanishes at all orders. 1. Introduction. In a recent paper [1] Osborn carried out a two-loop calculation of the β-function...

In this paper, we characterize N(k)-contact metric manifolds with generalized Tanaka-Webster connection. We obtain some curvature properties. It is proven that if an manifold connection K-contact then it example of Sasakian space form. Also, examine flatness and symmetric conditions concircular tensor on

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi–Civita connection of some semi-Riemannian metric on the group. As a special case, we will con...

We investigate necessary and sufficient conditions under which a nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given affine connection, and on the input-output behavior of the prolonged system...

Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been topic growing interest recent studies. Numerous works study cosmology symmetric assuming flat Friedmann-Lema\^itre-Robertson-Walker metric, while working so-called "coincident gauge", further that connection co...