Eugene V. Petrov

Eugene V. Petrov
V. N. Karazin Kharkiv National University · Department of Mathematics and Computer Science

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8
Publications
191
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6
Citations
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September 2008 - November 2016
V. N. Karazin Kharkiv National University
Position
  • Professor (Assistant)
September 2008 - November 2016
V. N. Karazin Kharkiv National University
Position
  • Professor (Assistant)

Publications

Publications (8)
Article
Full-text available
We obtain criteria for the harmonicity of the Gauss map of submanifolds in the Heisenberg group and consider the examples demonstrating the connection between the harmonicity of this map and the properties of the mean curvature field. Also, we introduce a natural class of cylindrical submanifolds and prove that a constant mean curvature hypersurfac...
Article
Full-text available
In this paper we find a criterion for the Gauss map of an immersed smooth submanifold in some Lie group with left invariant metric to be harmonic. Using the obtained expression we prove some necessary and sufficient conditions for the harmonicity of this map in the case of totally geodesic submanifolds in Lie groups admitting biinvariant metrics. W...
Article
Full-text available
In this paper we consider smooth oriented hypersurfaces in 2-step nilpotent Lie groups with a left invariant metric and derive an expression for the Laplacian of the Gauss map for such hypersurfaces in the general case and in some particular cases. In the case of CMC-hypersurface in the (2m+1)-dimensional Heisenberg group we also derive necessary a...

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