We want to find a measure of how ‘curved’ a curve is. Since this ‘curvature’ should depend only on the ‘shape’ of the curve, it should not be changed when the curve is reparametrized. Further, the measure of curvature should agree with our intuition in simple special cases. Straight lines themselves have zero curvature. Large circles should have smaller curvature than small circles which bend m...

INTRODUCTION Fatigue resistance of ProFile, Vortex Blue, and TRUShape files in artificial single curvature and in 2 different artificial double curvature canals was evaluated. METHODS Three files (ProFile, Vortex Blue [size 20/.06], and TRUShape [size 20/.06v]) were subjected to fatigue tests in a single curvature (group 1: 60° curvature) and 2 different double curvatures (group 2: 60° and 30...

We study Ollivier-Ricci curvature, a discrete version of Ricci curvature, which has gained popularity over the past several years and has found applications in diverse fields. However, the Ollivier-Ricci curvature requires an optimal mass transport problem to be solved, which can be computationally expensive for large networks. In view of this, we propose two alternative measures of curvature t...

The aim was to retrospectively determine the real incidence of congenital penile curvature in various forms of hypospadias, in order to indicate intraoperative assessment and correction of curvature. We analyzed 842 patients with hypospadias who underwent surgery from 2003 to 2010, classified into two groups. First group was intraoperatively checked for curvature as a routine procedure, while a...

The object of the present paper is to characterize K-contact Einstein manifolds satisfying the curvature condition R · C = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we study K-contact Einstein manifolds satisfying the curvature conditions C ·S = 0 and S ·C = 0, where S is the Ricci tensor. Finally, we consider K-contact Einstein manifolds sati...

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

Let M = M1 ×M2 be a product of complex manifolds. We prove that M cannot admit a complete Kähler metric with sectional curvature K < c < 0 and Ricci curvature Ric > d, where c and d are arbitrary constants. In particular, a product domain in Cn cannot cover a compact Kähler manifold with negative sectional curvature. On the other hand, we observe that there are complete Kähler metrics with nega...

In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we employ possible generalizations of the notion of Ricci curvature on Riemannian manifold to discrete spaces in order to infer certain robustness properties of...

the starting behavior of a supersonic axisymmetric mixed compression air intake was numerically investigated. the code solves reynolds-averaged navier–stokes equations using an explicit finite volume method in a structured grid by the roe flux difference splitting scheme. further, it uses the baldwin–lomax algebraic model to compute the turbulent viscosity coefficient. the correct method of sur...