Abstract The in situ and real-time measurement of curvature changes optically reflecting surfaces is a key element to better control bottom-up fabrication processes the semiconductor industry, but also follow or adjust mirror deformations during use for space optics industries. Despite progresses made last two decades thanks laser deflectometry-based techniques, community lacks an instrument, e...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

purpose : to evaluate the correlation of central corneal thickness (cct) with refractive error and keratometry in a group of patients eligible for laser keratorefractive surgery, which may serve as a bias in studies on intraocular pressure (iop) measurement methods : in a cross sectional observational study, the right eyes of 340 patients who underwent laser keratorefractive surgery during the ...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...