Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 1, 141-145.

Transnormal Graph Surfaces

A. M. d'Azevedo Breda, F. J. Craveiro de Carvalho

Graphs of smooth maps very often are examples of transnormal submanifolds of 
euclidian space \R$^n$. This fact gives us some motivation to look for 
conditions on the map which ensure us that the graph is transnormal or not.
In this note we
study maps $f\sp :\R^2 \rightarrow \R$. No doubt that our results 
(with the possible exception of Theorem 3.2 in {\bf 3}.) still hold when we 
replace \R$^2$ by \R$^n$. However what we gain from working in a more general 
context is very little. Our results depend heavily on results which have 
been established previously in [1] and [3].