Combining several previously known arguments, we prove marked length spectrum rigidity for surfaces with nonpositively curved Riemannian metrics away from a finite set of cone-type singularities with cone angles > 2π. With an additional condition, we can weaken the requirement on one metric to ‘no conjugate points.’

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

materials and methods: one hundred and thirty five mesial root canals of mandibular first and second molar teeth were selected. access cavities were prepared. after inserting a k-file size #10 into each canal, radiographs were taken. canal curvature was determined by measuring the schneider angle, canal access angle, as well as the canal radius, length, height and curvature starting distance on...

i ntroduction: the aim of this study was to compare the shaping ability of two single-file systems and conventional rotary instruments in severely curved root canals of extracted human molars. methods and materials: mesiobuccal canals of 120 mandibular molars with angles of curvature ranging between 25 ° and 35 ° and radii of curvature from 5 to 9 mm, were divided into three groups ( n =40). in...

although, most of the abnormal structures of human brain do not alter the shape of outer envelope of brain (surface), some abnormalities can deform the surface extensively. however, this may be a major problem in a surface-based registration technique, since two nearly identical surfaces are required for surface fitting process. a type of verification known as the circularity check for the shap...

introduction: the objective of this study was to compare the shaping ability of three rotary filing systems; constant taper k3 instruments, constant taper profile instruments and progressive taper protaper rotary instruments in clear resin blocks with simulated curved root canals. materials and methods: forty five resin blocks were divided into three groups. group a preparation was conducted wi...

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 ...