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.
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Reference
W. BLASCHKE, “Einführung in die Ceometrie der Waben”, Basel, 1955.
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n pencils of spheres are said to belong to the same bundle,if all the spheres cut a fixed sphere orthogonally.
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Erdogan, H.İ. Hexagonal-surface-webs formed by n-pencils of spheres belonging to the same bundle. J Geom 38, 39–41 (1990). https://doi.org/10.1007/BF01222893
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DOI: https://doi.org/10.1007/BF01222893