It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...

Arterial thoracic outlet syndrome (TOS) is a rare vascular abnormality. Its common cause is a cervical rib but it is seldom detected secondary to trauma of the clavicle, particularly in association with surgical repair of a fractured clavicle. An athletic 45-year-old man developed a recurrent ischaemic upper limb after repair to a non-union fractured clavicle. He underwent multiple separate pro...

We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition CD(K,N). We show also that for weighted Riemannian manifolds the tria...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

Objectives/Goals Considering the variety of spinal deformity treatments, many patients agree that after surgery their mobility is significantly reduced. The utilization of resorbable materials for anterior spinal fusion systems, patients will experience the success of spinal deformity treatment and retain their prior mobility. If the systems are used on vertebrae with larger anterior width, the...

the structure of the sheep cervix limits the application of reproductive biotechnologies such as embryo transfer and artificial insemination. the aim of this study was to determine differences in cervical anatomy and morphology between sanjabi lambs and ewes, and the relationship between cervical anatomy and cervical penetration in ewes. four hundred and sixty eight postmortum cervices belongin...

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].