Matemáticas Fundamentales

El miércoles 29 de octubre a las 12:00 el profesor Jürg Peter Buser impartirá la siguiente charla en el Departamento de Matemáticas de la UNED.

Título: Three-dimensional hyperbolic geometry and Löbell manifolds.

Resumen: In his 1840 work on the theory of parallels, Lobachevsky develops hyperbolic trigonometry from beautiful synthetic geometric arguments in three dimensions. In the first third of the lecture, we highlight elements of this little-known approach. Hyperbolic or non-Euclidean geometry gradually gained acceptance in the mathematical community, and in 1927, Löbell constructed the first closed surfaces that support this geometry. To do this, he used right-angled geodesic hexagons as building blocks. In 1931, he found a much rarer building block in space, which enabled him to construct the first three-dimensional compact hyperbolic manifold. We refer to the examples constructed in this way as Löbell manifolds and the building blocks used as Löbell polyhedra. We will introduce some of them in the second third of the lecture. In the last third, we return to trigonometry and use ‘Mathematica’ animations to show how such formulas can also be proven, even for Löbell polyhedra, using non-Euclidean rigid motions. Part of the lecture is from joint work with A. Vesnin and A. Mednykh