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Article
On Degenerate Orbits of Real Lie Algebras in Multidimensional Complex Spaces
The article studies (locally) holomorphically homogeneous real hypersurfaces of complex spaces. Currently, the problem of classifying such hypersurfaces is completely solved only in the spaces
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Article
On the Tubular Structure of Holomorphically Homogeneous Real Hypersurfaces in \(\boldsymbol{\mathbb{C}}^{\mathbf{4}}\)
In connection with the problem of describing holomorphically homogeneous real hypersurfaces in a complex space \(\mathbb{C}^{4}\) ...
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Article
On Orbits of 4-Dimensional Representations of 3-Dimensional Solvable Lie Algebras
In a 4-dimensional real space, we discuss linearly homogeneous hypersurfaces that are the orbits of 3-dimensional solvable Lie algebras. A complete list of inequivalent representations of a decomposable 3-dime...
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Article
On Linear Homogeneous Hypersurfaces in \({{\mathbb{R}}^{4}}\)
The problem of describing affinely homogeneous hypersurfaces in the space \({{\mathbb{R}}^{4}}\) that possess exact...
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Article
Decomposable Five-Dimensional Lie Algebras in the Problem on Holomorphic Homogeneity in ℂ3
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 m...
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Article
On Some Topological Characteristics of Harmonic Polynomials
In this paper, we study geometric and topological properties of harmonic homogeneous polynomials. Based on the study of zero-level lines of such polynomials on the unit sphere, we introduce the notion of their...
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Article
On Harmonic Polynomials Invariant under Unitary Transformations
Unitary transformations and canonical representatives of a family of real-valued harmonic fourth-degree polynomials in three complex variables are studied. The subject relates to the study of Moser normal e...
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Article
On the Problem of Describing Holomorphically Homogeneous Real Hypersurfaces of Four-Dimensional Complex Spaces
We discuss two fragments of a large problem that extends the author’s recently completed similar studies in the space \(\mathbb C^3\)
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Article
On Orbits of Action of 5-Dimensional Non-Solvable Lie Algebras in Three-Dimensional Complex Space
In 1932, E. Cartan described holomorphically homogeneous real hypersurfaces of two-dimensional complex spaces, but a similar study in the three-dimensional case remains incomplete. In a series of works perform...
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Article
On Holomorphic Realizations of Nilpotent Lie Algebras
Realizations of five-dimensional Lie algebras as algebras of holomorphic vector fields on homogeneous real hypersurfaces of a three-dimensional complex space are studied. In view of already known results, in t...
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Article
On holomorphic homogeneity of real hypersurfaces of general position in ℂ3
Holomorphically homogeneous strictly pseudoconvex real hypersurfaces of threedimensional complex spaces are studied within the coefficient approach. It is shown that the family of surfaces for which a fourth-d...
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Article
On complete list of affine homogeneous surfaces of (ɛ, 0)-types in the space ℂ3
The problem of description of affine homogeneous real hypersurfaces in complex spaces is an important part of the problem of holomorphic classification of homogeneous manifolds, which has no complete solution ...
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Article
Affine-homogeneous surfaces of type (0, 0) in the space ℂ3
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Article
Affinely homogeneous real hypersurfaces of ℂ2
A complete affine classification of germs of affinely homogeneous real hypersurfaces of ℂ2 is presented. The two main tools used in the classification are canonical local equations of manifolds and the theory of ...
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Article
Various representations of matrix lie algebras related to homogeneous surfaces
We construct a 3-parameter family of real homogeneous hypersurfaces in the 3-dimensional complex space. This family generalizes a series of examples published earlier. It contains Levi nondegenerate surfaces (...
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Article
On the affine homogeneity of tubular type surfaces in ℂ3
We present a systematic approach to solving the problem of affine homogeneity of real hypersurfaces in the three-dimensional complex space. This question is an important part of the general problem of holomorp...
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Article
Affine homogeneity of indefinite real hypersurfaces in the space ℂ3
We develop a constructive approach to the problem of describing affinely homogeneous real hypersurfaces in 3-dimensional complex space having nondegenerate sign-indefinite Levi form. We construct the affine in...
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Article
An example of a two-parameter family of affine homogeneous real hypersurfaces in ℂ3
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Article
Real subalgebras of small dimensions of the matrix lie algebra M(2, ℂ)
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Article
Calculation of the characteristics of radiative multiphoton absorption and emission lines when an atom interacts with pulsed laser radiation
We have used the quantum electrodynamic theory of moments and the S-matrix formalism of Gell-Mann and Low to carry out numerical modeling of the characteristics (shift, width) of radiative multiphoton absorpti...
