Українська версія

Faculty

Vladimir . DubovoyVladimir . Dubovoy Vladimir . Dubovoy Full professor of the department of pure mathematics, doctor of sciences in mathematics

Sergey . FavorovSergey . Favorov Sergey . Favorov Full professor of the department of pure mathematics, doctor of sciences in mathematics

Sergey . GefterSergey . Gefter Sergey . Gefter Associate professor of the department of pure mathematics, head of the department of pure mathematics, phd in mathematics

Vyacheslav . GordevskyyVyacheslav . Gordevskyy Vyacheslav . Gordevskyy Full professor of the department of pure mathematics, doctor of sciences in mathematics

Vladimir (Volodymyr) M. KadetsVladimir (Volodymyr) M. Kadets Vladimir (Volodymyr) M. Kadets Full professor of the department of pure mathematics, doctor of sciences in mathematics

Mariya . ShcherbinaMariya . Shcherbina Mariya . Shcherbina Professor of the department of pure mathematics

Dmitry . ShepelskyDmitry . Shepelsky Dmitry . Shepelsky Doctor of sciences in mathematics

Alexander L. YampolskyAlexander L. Yampolsky Alexander L. Yampolsky Professor of the department of pure mathematics, doctor of sciences in mathematics

Dmytry V. BolotovDmytry V. Bolotov Dmytry V. Bolotov Doctor of sciences in mathematics

Vasyl O. GorkavyyVasyl O. Gorkavyy Vasyl O. Gorkavyy Doctor of sciences in mathematics, associate professor

Alexander V. RezounenkoAlexander V. Rezounenko Alexander V. Rezounenko Professor of the department of pure mathematics, doctor of sciences in mathematics

Anna M. VishnyakovaAnna M. Vishnyakova Anna M. Vishnyakova Professor of the department of pure mathematics, doctor of sciences in mathematics

Tamara . FastovskaTamara . Fastovska Tamara . Fastovska Associate professor of the department of pure mathematics, phd in mathematics, associate professor

Nataliуa . GiryaNataliуa . Girya Nataliуa . Girya Associate professor of the department of pure mathematics, phd in mathematics

Oleksii . HukalovOleksii . Hukalov Oleksii . Hukalov Associate professor of the department of pure mathematics, phd in mathematics

Eugene . KarolinskyEugene . Karolinsky Eugene . Karolinsky Associate professor of the department of pure mathematics, phd in mathematics

Eugene V. PetrovEugene V. Petrov Eugene V. Petrov Phd in mathematics, senior lecturer

Aleksey . ShcherbinaAleksey . Shcherbina Aleksey . Shcherbina Phd in mathematics, senior lecturer

Olena O. ShugailoOlena O. Shugailo Olena O. Shugailo Phd in mathematics, senior lecturer

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Viktoria V. DavydovaViktoria V. Davydova Viktoria V. Davydova Engineer

Iryna V. KatsIryna V. Kats Iryna V. Kats Leading engineer

Thu Hien . NguyenThu Hien . Nguyen Thu Hien . Nguyen

Dmytro . SeliutinDmytro . Seliutin Dmytro . Seliutin

Olesia O. ZavarzinaOlesia O. Zavarzina Olesia O. Zavarzina Ph.d., associate professor

Eugene V. Petrov

Phd in mathematics, senior lecturer

Link on external publications: ResearchGate.

List of selected publications

A.A. Borisenko, E.V. Petrov Surfaces in the Three-Dimensional Heisenberg Group on Which the Gauss Map Has Bounded Jacobian // Mathematical Notes, 89 (2011), p. 746-748, 2011

E.V. Petrov The Gauss Map of Submanifolds in the Heisenberg Group // Differential Geometry and its Applications, 2011, vol. 29, p. 516–532, 2011

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 hypersurface with harmonic Gauss map is cylindrical.

Keywords: Heisenberg group, Gauss map, harmonic map, mean curvature field, constant mean curvature hypersurface

Ye.V. Petrov Submanifolds with the Harmonic Gauss Map in Lie Groups // Journ. of Math. Phys., An., Geom., 4 (2008), no. 2, p. 278-293, 2008

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. We show that, depending on the structure of the tangent space of a submanifold, the Gauss map can be harmonic in all biinvariant metrics or non-harmonic in some metric. For $2$-step nilpotent groups we prove that the Gauss map of a geodesic is harmonic if and only if is constant.

Keywords: Left invariant metric, biinvariant metric, Gauss map, harmonic map, $2$-step nilpotent group, totally geodesic submanifold

E.V. Petrov On the Gauss Map of Submanifolds in Lie Groups (in Russian) // Dopovidi NANU, 2008, 11, p. 28-31, 2008

Ye.V. Petrov The Gauss Map of Hypersurfaces in 2-Step Nilpotent Lie Groups // Journ. of Math. Phys., An., Geom., 2 (2006), no. 2, p. 186-206, 2006

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 and sufficient conditions for the Gauss map to be harmonic and prove that for $m=1$ all CMC-surfaces with the harmonic Gauss map are ''cylinders''.

Keywords: 2-step nilpotent Lie group, Heisenberg group, left invariant metric, Gauss map, harmonic map, minimal submanifold, constant mean curvature

L.A. Masal'tsev, E.V. Petrov On the Stability of Minimal Surfaces in the 3-Dimensional Heisenberg Group (in Russian) // Visnyk KhNU, 645, 2004, p. 135-141, 2004

L.A. Masal'tsev, E.V. Petrov Minimal Submanifolds in Heisenberg Groups (in Russian) // Visnyk KhNU, 602, 2003, p. 35-45, 2003