On homogeneity of embedded submanifolds
نویسنده
چکیده
We discuss in the paper the problem that is connected in their roots with the several variables complex analysis. But its study shows the actuality of the problem itself as well as the questins near to it for the many sections of modern mathematics, using or touching the notion of homogeneity. To exlain the interest of complex analysis to last term recall for example the classical Riemann theorem that asserts the holomorphic equivalence of unit circle to any simply connected domain (with ”large” boundary) of complex plane. In the case of several complex variables this theorem is not valid. One of the reasons of such fenomenon is the holomorphic distinction between the arbitrary domain boundary and the real sphere in C( 1). Moreover two arbitrary real hypersurfaces of the space C cannot be redused one to another by biholomorphic transformation. This principle is valid even in local situation. As a consequnce two germs of any surface (connected even with near its points) turn as a rule to be inequivalent from the holomorpic point of fiew. In this situation the interest to the ”exclusive” hypersurfaces is natural, that are ”the same” in all its points or (in strong terms) are homogeneous according to the holomorphic transformations.
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