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- W2070097282 abstract "In a former memoirt we developed a theory of transformations K of conjugate systems with equal point invariants into systems of the same kind. Subsequently$ we considered the case in which the lines joining corresponding points on two surfaces in the relation of a transformation K form a normal congruence. These surfaces, being of a particular kind, are called surfaces C. We have shown that there are transformations of the K type, denoted by Km I which transform a surface C into surfaces C. The surfaces S, orthogonal to these normal congruences, are the surfaces Q discussed by Demoulin.? We showed that there exist transformations Am of S into surfaces Si, such that S and a surface Si envelope a two-parameter family of spheres, and in the correspondence between S and Si thus established lines of curvature correspond. In the present memoir we extend our investigations concerning these transformations Am , and more particularly apply the results to certain types of surfaces Q. Transformations Am belong to the general class of transformations of Ribaucour, and in the first part of the paper we put the equations in a form possessed by all transformations of Ribaucour. Guichard discoveredfl a class of surfaces possessing the following characteristic property: If S is such a surface, there exists an associate surface Si such that the lines of curvature on the two surfaces have the same spherical representation, and the principal radii of curvature P1, P2 and p', p2 of the respective surfaces are in the relation" @default.
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- W2070097282 date "2005-12-20" @default.
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- W2070097282 title "Transformations of surfaces" @default.
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