# Alexander L. Yampolsky

Professor of the department of pure mathematics, doctor of sciences in mathematics

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 (2012)* //
Journal of Math. Phys., Analysis, Geom., 2012,
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

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

**Yampolsky A.**
*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.**
*Totally geodesic unit vector fields on Riemannian manifold* //
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

**Yampolsky A.**
*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.

**Abbassi M.T.K., Yampolsky A.**
*Transverse totally geodesic submanifolds of the tangent bundle.* //
Math. Publ. Debrecen,
v.64 /1-2, p. 129-154, 2004

**Yampolsky A., Saharova E. **
*Powers of the space form curvature operator and geodesics of the tangent bundle.* //
Ukr. Math. Journal,
v.56/9, p. 1231-1243, 2004

**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.**
*On the vertical strong-sphericity index of Sasaki metric of tangent sphere bundle.* //
Math. phys., analysis and geometry,
v.3, No ¾, p. 446-456, 1996

**Yampolsky A.**
*On the totally geodesic vector fields on submanifold* //
Math. phys., analysis and geometry,
v.1, No 3/4, pp. 540-545, 1994

**Yampolsky A.**
*On the strong sphericity index of Sasaki metric of tangent sphere bundle.* //
Ukr. geom. sbornik,
v.35, pp. 150-159, 1992

**Yampolsky A.**
*On characterisation of projections of geodesics of tangent (sphere) bundle of complex protective space.* //
Ukr. geom. sbornik,
v.34, pp. 121-126, 1991

**Yampolsky A., Borisenko A.A.**
*Riemannian geometry of bundles.* //
Uspehi math. nauk,
No 6, pp 51-95, 1991

**Yampolsky A., Borisenko A.A.**
*Riemannian geometry of bundles (in Russian)(and in Eng)* //
Uspehi math. nauk,
No 6, pp 51-95, 1991

**Yampolsky A.**
*On the extremal values of sectional curvature of Sasaki metric of tangent sphere bundle of constant curvature space.* //
Ukr. geom. sbornik,
v.32, pp. 127-137, 1989

**Yampolsky A.., Borisenko A.A.**
*The Sectional curvature of Sasaki metric of the T1Mn.* //
Ukr. geom. sbornik,
v.30 , pp.10-17, 1987

**Yampolsky A., Borisenko A.A.**
*On the Sasaki metric of tangent and normal bundle.* //
Dokl. Acad. Sci. USSR,
v. 294, No 1, pp. 19-22, 1987

**Yampolsky A., Borisenko A.A.**
*On the Sasaki metric of normal bundle of submanifold in Riemannian space.* //
Math. Sbornik,
v.134, No 2, pp. 158-176, 1987

**Yampolsky A.., Borisenko A.A.**
*Cylindricity of tangent bundles of strongly parabolic metrics and strongly parabolic surfaces.* //
Ukr. geom. sbornik,
v.29, p. 12-32, 1986

**Yampolsky A.**
*On the curvature of Sasaki metric of tangent sphere bundle.* //
Ukr. geom. sbornik,
v.28, p. 132-145, 1985

**Yampolsky A.**
*To the geometry of tangent sphere bundle of the Riemannian manifold.* //
Ukr. geom. sbornik, 1988,
v.24, p.129-132, 1981

Keywords: Sasaki metric, sectional curvature

**Yampolsky, A **
* Eikonal Hypersurfaces in the Euclidean n-Space. * //
Mediterranean Journal of Mathematics. 2017. 14: 160,

**Yampolsky A., Fursenko O.**
*Caustics of wave fronts reflected by a surface. * //
Mediterranean Journal of Mathematics. ,
2017. 14: 160,

**Yampolsky A., Opariy A.**
*Generalized helices in three dimensional Lie groups* //
Turkish Journal of Mathematics.,
2019. 43: 1447 – 1455. ,

**Yampolsky A.**
*Catacaustics of a hypersurface in the Euclidean n-space.* //
Mediterranean Journal of Mathematics.,
2019. 16: 88,

**Yampolsky A.**
*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.,