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Decomposable Five-Dimensional Lie Algebras in the Problem on Holomorphic Homogeneity in ℂ3

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In connection with the problem of describing holomorphically homogeneous real hypersurfaces in the space ℂ3, we study five-dimensional real Lie algebras realized as algebras of holomorphic vector fields on such manifolds. We prove the following assertion: If on a holomorphically homogeneous real hypersurface M of the space ℂ3, there is a decomposable, solvable, five-dimensional Lie algebra of holomorphic vector fields having a full rank near some point P ∈ M, then this surface is either degenerate near P in the sense of Levy or is a holomorphic image of an affine-homogeneous surface.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    A. V. Atanov & A. V. Loboda

  2. Voronezh State Technical University, Voronezh, Russia

    A. V. Atanov & A. V. Loboda

Authors
  1. A. V. Atanov
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  2. A. V. Loboda
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Correspondence to A. V. Atanov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.

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Atanov, A.V., Loboda, A.V. Decomposable Five-Dimensional Lie Algebras in the Problem on Holomorphic Homogeneity in ℂ3. J Math Sci 268, 84–113 (2022). https://doi.org/10.1007/s10958-022-06182-3

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