Some Properties of Potential Surfaces

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where px and f\ denote the principal radii of S. For the second of the conditions (5) this gives p1 = />2, that is, S is a sphere, when real. Combining these results we have that minimal surfaces and spheres are the only real surfaces for which the spherical representation of lines of length zero is the system of rectilinear generatrices of the sphere. In order to determine what surfaces have the lines of length zero on the sphere for spherical representation of its asymptotic lines we note that for the parameters used previously the equation of the asymptotic directions is*

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تاریخ انتشار 2007