, Volume 58, Issue 2, pp 203-212

Smooth projective translation planes

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Abstract

A projective plane is called smooth if both the point space and the line space are smooth manifolds such that the geometric operations are smooth. We prove that every smooth projective translation plane is isomorphic to one of the classical planes over ℝ, ℂ, ℍ or \(\mathbb{O}\) .

Dedicated to Professor Dr. H. Salzmann on the occasion of his 65th birthday