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- Title
Decomposable Five-Dimensional Lie Algebras in the Problem on Holomorphic Homogeneity in ℂ<sup>3</sup>.
- Authors
Atanov, A. V.; Loboda, A. V.
- Abstract
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.
- Subjects
VECTOR fields; VECTOR algebra; HOMOGENEITY; C*-algebras; LIE algebras; HYPERSURFACES
- Publication
Journal of Mathematical Sciences, 2022, Vol 268, Issue 1, p84
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-022-06182-3