Homogeneous Surfaces in C4 Associated with a 5-Dimensional Completely Nondegenerate Cubic Model Surface of CR-Type (1; 3)статья
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Аннотация:The action on the space C4 of the 7-dimensional Lie group of infinitesimal holomorphicautomorphisms of a completely nondegenerate cubic model surface Q of CR-type (1; 3) is considered.All orbits of the given action are found and their biholomorphic classification is given. One of the orbitscoincides with the surface Q (the 5-dimensional orbit), two orbits are 6-dimensional, and the remainingpart of the space C4, the complement to the above orbits, foliates into 7-dimensional real orbits. It isalso proved that the algebra of infinitesimal holomorphic automorphisms of all orbits, except for thetwelve holomorphically degenerate orbits, coincides with the algebra of the surface Q.