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Vladimir Ezhov

Publications and source records attributed to Vladimir Ezhov.

9 recordsLinked to original sources
arXiv2024

On the classificarion of 3-dimensional spherical Sasakian manifolds

In this article we consider spherical hypersurfaces in $\mathbb C^2$ with a fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish the correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, the parameters used in Stanton's description of rigid spheres, and the parameters arising from the rigid normal forms. We also geometrically describe the moduli space for rigid spheres, and provide geometric distinction between Stanton's hypersurfaces and those found by Ezhov and Schmalz. Finally, we determine the Sasakian automorphism groups of the rigid spheres and detect the homogeneous Sasakian manifolds among them.

math.DG↗
arXiv2013

Explicit description of spherical rigid hypersurfaces in C^2

We provide an explicit description of all rigid hypersurfaces that are equivalent to a Heisenberg sphere. These hypersurfaces are determined by 4 real parameters. The defining equations of the rigid spheres can also be viewed as the complete solution of a non-linear PDE that expresses the vanishing Cartan curvature condition for rigid hypersurfaces.

math.CV↗
arXiv2005

Elliptic CR-manifolds and shear invariant ODE with additional symmetries

We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold.

math.CV↗
arXiv2005

Canonical Cartan connection and holomorphic invariants on Engel CR manifolds

We describe a complete system of invariants for 4-dimensional CR manifolds of CR dimension 1 and codimension 2 with Engel CR distribution by constructing an explicit canonical Cartan connection. We also investigate the relation between the Cartan connection and the normal form of the defining equation of an embedded Engel CR manifold.

math.CV↗
arXiv2004

Towards a Classification of Homogeneous Tube Domains in C^4

We classify the tube domains in C^4 with affinely homogeneous base whose boundary contains a non-degenerate affinely homogeneous hypersurface. It follows that these domains are holomorphically homogeneous and amongst them there are four new examples of unbounded homogeneous domains (that do not have bounded realisations). These domains lie to either side of a pair of Levi-indefinite hypersurface. Using the geometry of these two hypersurfaces, we find the automorphism groups of the domains.

math.CV↗
arXiv2000

Cayley Hypersurfaces

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.

math.DG↗