CLASSIFICATION OF RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Ruled surfaces with the Gauss map satisfying a partial differential equation which is similar to an eigenvalue problem in a 3-dimensional Euclidean space are studied. Such a Gauss map is said to be of pointwise 1-type, namely, the Gauss map G satisfies Delta G = f(G + C), where Delta is the Laplacian operator, f is a non-zero function and C is a constant vector. As a result, such ruled surfaces are completely determined by the function f and the vector C when their Gauss map is of pointwise 1-type New examples of ruled surfaces called cylinders of an infinite type and rotational ruled surfaces are introduced in this regard