On orbits of action of 5-dimensional non-solvable Lie algebras in three-dimensional complex space

A. V. Atanov, I. G. Kossovskiy, A. V. Loboda
2019 Doklady Akademii Nauk  
After the description by E. Cartan in 1932 holomorphically homogeneous real hypersurfaces of two-dimensional complex spaces, a similar study in the 3-dimensional case remains incomplete. In a series of works performed by several international teams of authors, the problem is reduced to describing homogeneous surfaces that are non-degenerate in Levi sense and have exactly 5-dimensional Lie algebras of holomorphic vector fields. In this paper, precisely such homogeneous surfaces are investigated.
more » ... At the same time, a significant part of the extensive list of abstract 5-dimensional Lie algebras does not provide new examples of homogeneity. A complete description of the orbits of 5-dimensional non-solvable Lie algebras in a three-dimensional complex space, given in the paper, includes examples of new homogeneous hypersurfaces. The presented results bring to finish a large-scale scientific study of interest to various branches of mathematics.
doi:10.31857/s0869-56524876607-610 fatcat:hnak64yatbbtjiyfs2rp6d2ybe