Abstract We study the ergodic properties of horospheres on rank 1 manifolds with non-positive curvature. prove that are equidistributed under action geodesic flow towards Bowen–Margulis measure, a large class manifolds. In case surfaces, we define parametrization horocyclic set horocycles containing vector is recurrent flow. in restriction to this uniquely ergodic. The results valid for classes...

We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a 4-orbifold with vanishing first Betti number second at most as large the original one.

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r = N , there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter α goes to zero. Fur...

introduction: complete knowledge of root canal curvature is a critical factor in successful dental treatment .the aim of this study was to investigate the direction, radius and degree of curvature of maxillary anterior teeth and the relation between radius and degree of curvature in babol city. methods &materials;: this study was performed on 242 anterior teeth radiographs were taken by periapi...

We work primarily in the category of manifolds of bounded geometry. The objects are manifolds with bounds on the curvature tensor, its derivatives, and on the injectivity radius. The morphisms are diffeomorphisms of bounded distortion. We think of these manifolds as having a chosen bounded distortion class of metrics. Unless otherwise stated, all manifolds in the paper are assumed of this type....

let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...