Line congruence and transformation of projective surfaces
نویسنده
چکیده
The aim of this article is to present and reformulate systematically what is known about surfaces in the projective 3-space, in view of transformations of surfaces, and to complement with some new results. Special emphasis will be laid on line congruences and Laplace transformations. A line congruence can be regarded as a transformation connecting one focal surface with the other focal surface. A Laplace transformation is regarded as a method of constructing a new surface from a given surface by relying on the asymptotic system the surface is endowed with. The most interesting object in this article is a class of projectively minimal surfaces. We clarify the procedure of getting new projectievely minimal surfaces from a given one, which was proved by F. Marcus, as well as the procedure of Demoulin transformation of projective surfaces.
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