The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this tensor are compared with eigendirections of the material metric. Examples concerning spherically symmetric and axially symmetric space-times are then presented.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.

In this paper, we study certain curvature conditions satisfying by the conharmonic curvature tensor in a Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection. AMS Mathematics Subject Classification (2010): 53B05, 53C25

Let ∇ be a metric connection with totally skew-symmetric torsion T on a Riemannian manifold. Given a spinor field Ψ and a dilaton function Φ, the basic equations in type II B string theory are ∇Ψ = 0 , δ(T) = a · (

We obtain results on the vanishing of divergence of Riemannian and Projective curvature tensors with respect to semi-symmetric metric connection on a trans-Sasakian manifold under the condition φ(gradα) = (n− 2)gradβ.

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic concurrent conformal vectorfields projective fields on with respect to thesemi-symmetric }$ obtain someproperties related them.