Geodesic
Decomposable five-dimensional Lie algebras in the problem of holomorphic homogeneity in~$\mathbb{C}^3$
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 86-115

Voir la notice de l'article provenant de la source Math-Net.Ru

In connection with the problem of describing holomorphically homogeneous real hypersurfaces in the space $\mathbb{C}^3$, we study five-dimensional real Lie algebras realized as algebras of holomorphic vector fields on such manifolds. We prove that if on a holomorphically homogeneous real hypersurface $M$ of the space $\mathbb{C}^3$, there is a decomposable, solvable, five-dimensional Lie algebra of holomorphic vector fields having a full rank near some point $P\in M$, then this surface is either degenerate near $P$ in the sense of Levy or is a holomorphic image of an affine-homogeneous surface.
Keywords: homogeneous manifold, holomorphic transformation, vector field, real hypersurface in $\mathbb{C}^3$.
Mots-clés : decomposable Lie algebra 
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     author = {A. V. Atanov and A. V. Loboda},
     title = {Decomposable five-dimensional {Lie} algebras in the problem of holomorphic homogeneity in~$\mathbb{C}^3$},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {86--115},
     publisher = {mathdoc},
     volume = {173},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a7/}
}
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A. V. Atanov; A. V. Loboda. Decomposable five-dimensional Lie algebras in the problem of holomorphic homogeneity in~$\mathbb{C}^3$. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 86-115. http://geodesic.mathdoc.fr/item/INTO_2019_173_a7/