On Certain Pairs of Surfaces in Ordinary Space
نویسنده
چکیده
where k denotes a constant; (2) The curves of J are a linear system; that is, a point transformation exists which converts them into the straight lines of a plane. I t is natural to inquire what class of surfaces we shall obtain if, instead of using property (2), we make the less specific demand that a point transformation exists which converts the curves of J into the geodesies of another surface. Here we have found certain pairs of surfaces S and Si which furnish the complete solution of our generalized problem. According to whether the constant k is zero or not, the linear elements of S and Si take different types, whose derivation constitutes the purpose of the present paper.
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