We prove that a smooth projective complex surface X, not necessarily minimal, contains h(X) − 1 disjoint (−2)-curves if and only if X is isomorphic to a relatively minimal ruled rational surface F2 or P or a fake projective plane. We also describe smooth projective complex surfaces X with h(X) − 2 disjoint (−2)-curves.

This paper presents a generalized integrated framework of semi-automatic surgical template design. Several algorithms were implemented including the mesh segmentation, offset surface generation, collision detection, ruled surface generation, etc., and a special software named TemDesigner was developed. With a simple user interface, a customized template can be semi- automatically designed accor...

We give an upper bound of the slope for finite cyclic covering fibrations elliptic surface which includes bielliptic fibrations. also triple a ruled and hyperelliptic fibrations, provides new proof Xiao's bound.

Given a point and a rational curve in the plane, their bisector curve is rational 2]. However, in general, the bisector of two rational curves in the plane is not rational 3]. Given a point and a rational space curve, this paper shows that the bisector surface is a rational ruled surface. Moreover, given two rational space curves, we show that the bisector surface is rational (except for the de...

With the help of the Frenet frame of a given pseudo null curve, a family of parametric surfaces is expressed as a linear combination of this frame. The necessary and sufficient conditions are examined for that curve to be an isoparametric and asymptotic on the parametric surface. It is shown that there is not any cylindrical and developable ruled surface as a parametric surface. Also, some inte...

This paper presents and compares methods of error metrics used to measure the error for the flank milling of a machined ruled surface. The aim of this work is to propose a new scheme for error approximation that is easy to implement and gives better error assessment when using optimization techniques to determine tool position. We propose using as the error calculation an approximation to the d...

Introduction. Let a non-ruled surface 5 be referred to its asymptotic net as parametric. As a point Py moves along a curve C\ of S, the tangents at Py to the uand ^-asymptotic curves of 5 describe two ruled surfaces R" and R{> respectively. Let Sp and S, denote arbitrary transversal surfaces of the congruences of uand ^-tangents of S, respectively. The purpose of the present paper is to introdu...

(i) Gromov’s Compactness Theorem for pseudo-holomorphic curves in symplectic manifolds ([23]) and the topology of symplectomorphism groups of rational ruled surfaces (sections 2 and 3, references [1, 2]). (ii) Atiyah-Guillemin-Sternberg’s Convexity Theorem for the moment map of Hamiltonian torus actions ([9, 25]) and Kähler geometry of toric orbifolds in symplectic coordinates (sections 4 and 5...

Abstract In recent years, 3D data has been widely used in archaeology and the field of conservation restoration cultural properties. Virtual restoration, which reconstructs original state virtual space, is one promising applications utilizing scanning data. Though many studies have conducted, it still challenging to restore properties that consist multiple deformable components because not feas...