A basic question in geometry is to understand compact locally homogeneous manifolds, i.e., those compact manifolds that can be locally modelled on a homogeneous space J\H of a finite-dimensional Lie group H. This means that there is an atlas on a manifold M consisting of local diffeomorphisms with open sets in J\H where the transition functions between these open sets are given by translations ...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

Two Riemannian manifolds are said to have C-conjugate geodesic flows if there exist an C diffeomorphism between their unit tangent bundles which intertwines the geodesic flows. We obtain a number of rigidity results for the geodesic flows on compact 2-step Riemannian nilmanifolds: For generic 2-step nilmanifolds the geodesic flow is C rigid. For special classes of 2-step nilmanifolds, we show t...

We study an inverse problem for a non-compact Riemannian manifold whose ends have the following properties : On each end, the Riemannian metric is assumed to be a short-range perturbation of the metric of the form (dy) + h(x, dx), h(x, dx) being the metric of some compact manifold of codimension 1. Moreover one end is exactly cylindrical, i.e. the metric is equal to (dy) +h(x, dx). Given two su...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

We study models of axi-dilaton gravity in space-time geometries with torsion. We discuss conformal rescaling rules in both Riemannian and non-Riemannian formulations. We give static, spherically symmetric solutions and examine their singularity behaviour. PACS numbers: 04.50.+h, 04.20.Jb, 04.70.Bw E.mail: [email protected] E.mail: [email protected] 1

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

Let (M, F) be a closed foliated manifold, dimM = n, dimF = p, p+q = n, equipped with a Riemannian metric gM . We assume that the foliation F is Riemannian, and the metric gM is bundle-like. Let F = TF be the integrable distribution of tangent p-planes to F , and H = F⊥ be the orthogonal complement to F . The decomposition of TM into a direct sum, TM = F ⊕ H , induces a decomposition of the metr...

A notion of quasi-regularity is extended for the inclusion problem F(p) ∈ C , where F is a differentiable mapping from a Riemannian manifold M to Rn . When C is the set of minimum points of a convex real-valued function h on Rn and DF satisfies the L-average Lipschitz condition, we use the majorizing function technique to establish the semi-local convergence of sequences generated by the Gauss-...