Full Length Research Paper

A characterization of the projective transformation

Yasemin Alagöz* and Ziya Soyuçok

Yildiz Technical University, Department of Mathematics, Davutpasa, 34210, Esenler, Istanbul, Turkey.

*Corresponding author. E-mail: ygulluk@yildiz.edu.tr.

Accepted 4 December, 2009

   Abstract

We consider the transformations preserving the asymptotic directions of hypersurfaces in n-dimensional Euclidean space and we obtain the following characterization of the projective transformation: In n-dimensional Euclidean space, a transformation preserves the asymptotic directions of hypersurfaces if and only if it is the projective transformation.

Key words: Projective transformation, hypersurfaces, asymptotic directions.