Web site: http://geometry.univer.kharkov.ua
The department of geometry was founded in 1921. The first research in geometry at Kharkiv university was done by outstanding Russian geometer of the last quarter of the nineteenth century Konstantin Alekseevish Andreev (1848 – 1921). He worked at Kharkiv university from 1873 to 1898. In 1879 he became one of the founding members of the Kharkiv mathematical society.
Dmitry Matveevich Sintsov (1867 – 1946) was the first head of the department. He organized the mathematical cabinet of the university, collected a wonderful library and a rich set of geometric models. Yakov Pavlovich Blank (1903 – 1988) was the head from 1946 to 1950 and from 1959 to 1980.
From 1950 to 1959 academician Aleksey Vasilievich Pogorelov (1919 – 2002) headed the department. He devoted mush attention to the problems of teaching mathematics at school and at the university. Created in the eighties, the set of handbooks for the secondary school is the peak of his teaching activity.
From 1980 on Borisenko Alexander Andreevich, professor, Corresponding Member of the National Academy of Sciences of Ukraine is the head of the department.
The research seminar in geometry works at the department from 1921 (and holds on from 1945 continuously).
Basic fields of scientific researches of the department are:
Geometry of submanifolds in Finsler spaces (A.A. Borisenko, E.A. Olin);
Mean curvature flows (A.A. Borisenko);
Geometry of foliations and distributions (A.L. Yampolsky, D.V. Bolotov);
Harmonic maps and the Gauss map in Lie groups (E.V. Petrov);
Geometry of submanifolds in the Heisenberg group, geometry in large in Thurston three-dimensional geometries (A.A. Borisenko, E.V. Petrov);
Convex submanifolds in Riemannian spaces (A.A. Borisenko, D.I. Vlasenko);
The Gaussian image of submanifolds (A.A. Borisenko, O.V. Lykova, V.A. Gorkavyy);
Piecewise functions and its applications to the geometric modeling, mechanics and mathematical physics (P.G. Dolya);
The department provides teaching the following general courses: analytical geometry, differential geometry, topology, foundations of geometry, discrete mathematics, algebra and geometry.
There are two specializations at the department, namely “geometry” and “computer graphics and computer geometry”.
The special courses at the specialization “geometry” are «Software package Maple on PC», «Classical problems of geometry in the large», «Riemannian geometry», «Global Riemannian geometry», «Geometry of submanifolds», «Topology of foliations», «Computational geometry», «The Gaussian image of multidimensional manifolds», «Algebraic topology», «Exterior differential systems and their applications», «Geometry of Lie groups», «Geometric transformations», «Foundations of Finsler geometry», «Geometric foundations of physics», «Homogeneous and symmetric spaces», «Mean curvature flows».
The special courses at the specialization “computer graphics and computer geometry” are «Foundations of mathematical computations in Mathematica», «Raster and vector graphics», «Computer methods of Riemannian geometry», «Extension packages and the foundations of programming in Mathematica and Maple», «Geometry of submanifolds», «Algorithms of the computational geometry», «Analytical methods of geometric modeling», «Geometry of Lie groups», «Geometric aspects of artificial intelligence», «Foundations of mathematic modeling and computational experiment», «Creation of extension packages and plug-ins for the engineer computer graphic systems, office and mathematical packages», «Modern systems of geometric modeling», «Mean curvature flows».
Handbooks «Analytical geometry» by A.A. Borisenko and L.N. Ushakova («Osnova» publisher, 1993) and «Differential geometry and topology» by A.A. Borisenko («Osnova» publisher, 1995) were created at the department.