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Introduction. It is the purpose of this paper to establish certain transformations for any non-developable surface that bears a family of asymptotic curves and is immersed in a space of n dimensions Sn (n>3). All surfaces mentioned hereafter will belong to 5". The ambient of the osculating planes at a point of a surface to all of the curves on the surface that go through the point is a space of not more than five dimensions, f The class of all surfaces in Sn for which the ambient at all pointsdoi:10.2307/1990045 fatcat:2gomauqko5brhevkz7jphcminm