In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature, which is understood as the limit of the Ricci curvature of finite-dimensional groups, is calculated. We show that for some of these groups the Ricci curvatu...

where ω̃ = ( √ −1/2)g̃ij̄dz ∧ dz and Σ̃ = ( √ −1/2)R̃ij̄dz ∧ dz are the Kähler form, the Ricci form of the metric g̃ respectively, while c1(M) denotes the first Chern class. Under the normalized initial condition (2), the first author [3] (see also Proposition 1.1 in [4]) showed that the solution g(x, t) = ∑ gij̄(x, t)dz dz to the normalized flow (1) exists for all time. Furthermore by the work of Mok ...

Let f : X −→ S be a smooth projective family and let (L, h) be a singular hermitian line bundle on X with semipositive curvature current. Let Ks := K(Xs, KXs +L | Xs, h | Xs)(s ∈ S) be the Bergman kernel of KXs +L | Xs with respect to h | Xs and let hB the singular hermitian metric on KX + L defined by hB |Xs := 1/Ks. We prove that hB has semipositive curvature. This is a generalization of the ...

STUDY DESIGN Prospective study. OBJECTIVES To analyze the sagittal balance after single-level cervical disc replacement (CDR) and range of motion (ROM). To define clinical and radiologic parameters those have a significant correlation with segmental and overall cervical curvature after CDR. SUMMARY OF BACKGROUND DATA Clinical outcomes and ROM after CDR with Mobi-C (LDR, Troyes, France) pros...

background with the advent of hystroscopic surgery, abnormalities confined to the uterine cavity such as endometrial polyps, submucous myomas, uterine septae and synechia , were supposed to be treated effectively. diagnostic hysteroscopy is the gold standard for investigating the intrauterine diseases as it allows for biopsy and removal of lesions. objectives forty premenopausal women without t...

our case was a 48-year-old man with cervical pain radiatingto the upper limbs. imaging showed an intradural tumor with extradural component encasing the vertebral artery.thetumor diagnosed asa neurinomaand had been removed surgically.the post operationmagnetic resonance imagingshowed that the tumor was completely removed andthe vertebral arterywas intact at theentire length.the goal of surgery ...

abstract our patient was a 43-year-old woman with a suboccipital headache and pain in the upper cervical region from 3 years ago with a progressive generalized weakness in the last 3 months. neuroimaging study showed a dumbell shaped lesion with compression of the spinal cord in the cervical region that was identified as a neurinoma. the tumor had been completely removed by surgery but after th...

The female part of the population suffers more Whiplash Associated Disorders (WAD) in car crashes than males. Several studies have illustrated the need to consider the female population when developing and assessing the WAD prevention performance of advanced restraint systems in rear-end collisions. Presently only one crash test dummy is available, the average sized male BioRID. Recently a virt...