Russell's hypersurface from a geometric point of view

Abstract

The famous Russell hypersurface is a smooth complex affine threefold which is diffeomorphic to a euclidean space but not algebraically isomorphic to the three dimensional affine space. This fact was first established by Makar-Limanov, using algebraic minded techniques. In this article, we give an elementary argument which adds a greater insight to the geometry behind the original proof and which also may be applicable in other situations.