Hexagonal-surface-webs formed by n-pencils of spheres belonging to the same bundle

Abstract

In this work,it is shown that n pencils of spheres which belong to the same bundle form a hexagonal-surface-web.Firstly,4 pencils of spheres orthogonal to the same sphere are taken into consideration. Later,by means of a suitable transformation,the equations of these 4 pencils of spheres are written in their simplest form and the equation of the surface web is obtained.Then,it is concluded that any 4- pencils of spheres belonging to the same bundle form a hexagonal-surface-web.From this we conclude that a surface n-web which is formed by n pencils of spheres belonging to the same bundle is a hexagonal web.