ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 51,53 Erdogan, Hakki̇ Ismail, Istanbul Technical University, Turkey On a class of hexagonal-surface-web of spheres In this work, we consider four one-parameter families of spheres which do not belong to the same bundle with the additional condition that the three families of spheres cut the spheres of the fourth family in a hexagonal threeweb formed by the three families of curves defined by the equations

x^{2} + y^{2} − a^{2} − u_{1}.y = 0, x^{2} + y^{2} − u_{2} = 0, y − u_{3}.x = 0, (a ∈ R, a ≠ 0).

Then, we determine these four families of spheres so that they form a surface 6-web. Reference: H. I. Erdogan, Triples of circle-pencils forming a hexagonal threeweb in E^{2}, Journal of Geometry 35 (1989), 39-65.