
ВИДЕОТЕКА 
27th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications



Homogeneous real hypersurfaces in A. V. Loboda^{} ^{} Voronezh State Technical University 

Аннотация: The complete classification of holomorphically homogeneous real hypersurfaces in twodimensional complex spaces (in local and global forms) was proposed by E. Cartan in 1932. Final classification of locally homogeneous hypersurfaces in complex spaces of the following dimension essentially uses the properties of the degeneracy or nondegeneracy of Levi form of the surfaces under study. An important role is also played by the dimensions estimate In accordance with this estimate, all homogeneous nondegenerate surfaces with 8 and 7dimensional (Loboda 2001), and then with 6dimensional Lie algebras (DubrovMedvedevThe2017) were described. Levidegenerate homogeneous surfaces were completely studied in 2008 by Fels and Kaup. The report discusses the final part of classification associated with nondegenerate homogeneous surfaces having only trivial stabilizers. Individual blocks of the volumetric classification of abstract 5dimensional Lie algebras (Mubarakzyanov1961) were associated with the problem of homogeneity by studying holomorphic realizations of such algebras. In addition to the previously known homogeneous manifolds, there are only three (cited in the report) new types of holomorphically homogeneous real hypersurfaces. All these new examples are indefinite (nondegenerate) surfaces. In general, the studied family of homogeneous hypersurfaces splits into 40 types of manifolds; many of them, but not all, are holomorphically equivalent to tubular manifolds. The maximum dimension of the moduli spaces for the individual components of this family is 2. The presented results were obtained jointly with Akopyan R.S., Atanov A.V., Kossovskiy I.G. The study was supported by the RFBR grant № 170100592a. Язык доклада: английский 