# Alexander L. Yampolsky

Docent (associate professor) of department of fundamental mathematics, z, doctor of sciences in physics and mathematics, docent (associate professor)

Link on external publications: scholar.google.com.ua.

## List of selected publications

**A. Yampolsky**
*On stability of left invariant totally geodesic unit vector fields on three dimensional Lie group* //
Geometry and its Applications , Springer Proceedings in Mathematics & Statistics, Rovenski, Vladimir, Walczak, Paweł (Eds.) ,
2014, Vol. 72 , p. 167 - 195, 2013

Keywords: Sasaki metric, Lie group, stable submanifold

**Yampolsky A.**
*On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kahlerian manifold.* //
Journal of Math. Phys., Analysis, Geom.,
v. 8/2, p. 177-189, 2012

Keywords: Sasaki metric, Kahlerian manifold, tangent bundle, geodesics.

**Yampolsky A.**
*Minimal and totally geodesic sections of the unit sphere bundles.* //
Visnyk KhNU, ser. Math. App. Math and Mech. ,
v. 1030, p. 54 – 70, 2012

*Totally geodesic vector fields on pseudo-Riemannian manifolds.* //
Visnyk Kharkiv Karazin Univ., ser Math, App. Math and Mech, ,
v. 990, p. 4 - 14, 2011

*Invariant totally geodesic unit vector fields on three-dimensional Lie groups* //
Journal of Mathematical Physics, Analysis, Geometry,
vol. 3, No. 2, pp. 253 - 276, 2007

Keywords: Sasaki metric, totally geodesic unit vector eld, almost contact structure, Sasakian structure.

**Yampolsky A.**
//
Dokl. Ukr. Acad Nauk,
v.3, p. 32-35, 2005

*Totally geodesic submanifolds in the tangent bundle of a Riemannian 2-manifold.* //
Journal of Mathematical Physics, Analysis, Geometry,
v.1/1, p. 116-139, 2005

*On special types of minimal and totally geodesic unit vector fields.* //
7-th International Conference on Geometry, Integrability and Quantization, June 2-10, Varna (Bulgaria), SOFTEX, Sofia,
p. 290 – 304, 2005

Keywords: Sasaki metric, minimal unit vector ﬁeld, totally geodesic unit vector ﬁeld, strongly normal unitvector ﬁeld,Sasakian space form.

**A. Yampolsky**
*Full description of totally geodesic unit vector field on Riemannian 2-manifold.* //
Matematicheskaya fizika, analiz, geometriya,
2004, v.11/3, p.355-365, 2004

Keywords: Sasaki metric, totally geodesic unit vrctor field

**A. Yampolsky**
*Totally geodesic property of the Hopf vector field.* //
Acta Math. Hungarica,
2003, v.101, № 1-2, p. 73-92, 2003

Keywords: Sasaki metric, Hopf vector field, curvature

**A. Yampolsky**
*On extrinsic geometry of unit normal vector field of Riemannian hyperfoliation.* //
Math. Publ. Debrecen,
v.63/4, p. 555-567, 2003

Keywords: Sasaki metric, hyperfoliation

**A. Yampolsky **
*On the mean curvature of a unit vector field.* //
Math. Publ. Debrecen,
v.60, 1/2, p. 131-155, 2002

Keywords: Sasaki metric, minimal unit vector field

**A. Yampolsky**
*On the intrinsic geometry of a unit vector field.* //
Comment. Math. Univ. Carolinae 2002,,
v.43, № 2, p. 299-317, 2002

Keywords: Sasaki metric, totally geodesic submanifold

**Yampolsky A.**
//
Math. phys., analysis and geometry,
v.3, No ¾, p. 446-456, 1996

**Yampolsky A.**
//
Math. phys., analysis and geometry,
v.1, No 3/4, pp. 540-545, 1994

**Yampolsky A.**
//
Ukr. geom. sbornik,
v.32, pp. 127-137, 1989

**Yampolsky A.., Borisenko A.A.**
//
Ukr. geom. sbornik,
v.29, p. 12-32, 1986

**Yampolsky A.**
*To the geometry of tangent sphere bundle of the Riemannian manifold.* //
Ukr. geom. sbornik,
v.24, p.129-132, 1981

Keywords: Sasaki metric, sectional curvature

//

**A. Yampolsky A, O.Fursenko**
* Caustics of wave fronts reflected by a surface* //
Journal of Mathematical Sciences and Modeling,
2018, V 1 , Issue 2, Pages 131 - 137. https://doi.org/10.33187/jmsm.431543,

**A. Yampolsky, A. Opariy **
*Generalized helices in three-dimensional Lie groups* //
, Turkish Journal of Mathematics (2019) ,
43: 1447 – 1455. http://journals.tubitak.gov.tr/math/,

**A. Yampolsky**
* Catacaustics of a hypersurface in the Euclidean n-space. * //
Mediterranean Journal of Mathematics, ,
(2019) 16: 88. https://doi.org/10.1007/s00009-019-1365-3,

**A. Yampolsky**
*On Projective Classication of Points of a Submanifold in the Euclidean Space. * //
Journal of Mathematical Physics, Analysis, Geometry.,
2020. V. 16, № 3, P. 364–371. ,

**A. Yampolsky**
*On properties of the Reeb vector field of (α,β) trans-Sasakian structure. * //
Turkish Journal of Mathematics, 2022,,
Vol. 46: No. 6, Article 19. ,