On the surfaces of Lorentz manifold whose normal bundles have special properties (Q799248)

Let S be a surface of the manifold \({\mathbb{R}}^ 3\) provided with the Lorentz metric \(ds^ 2=dx^ 2+dy^ 2-dz^ 2\). The aim of the present paper is to study such a surface S having the property that its normals establish an area preserving representation between the two sheets of the evolute \(S_ 1\), \(S_ 2\) of S. The main results can be stated as follows. The catenoid is the only minimal surface of the Lorentz manifold defined above with this property.