Person: Reeb, Georges Henri
Georges Reeb was a French mathematician who worked in differential topology, differential geometry, topological dynamics and non-standard analysis.
Mathematical Profile (Excerpt):
- Reeb began his university studies at the University of Strasbourg before the start of World War II.
- Reeb was part of the evacuation and continued his studies in Clermont-Ferrand.
- Reeb, like all the staff and students, had to endure difficult times during the occupation.
- The advisor for Reeb's doctoral work at Clermont-Ferrand was Charles Ehresmann who, like Reeb, was an Alsatian.
- Ehresmann had only been appointed to Strasbourg shortly before the university moved to Clermont-Ferrand and Reeb was his second doctoral student.
- This papers studies fields of ppp-dimensional elements of contact in a differentiable manifold and, in 1945, Reeb published a single authored paper Sur les variétés intégrales des champs d'éléments de contact complètement intégrables Ⓣ(On integral manifolds of fields of fully integrated contact elements) which extended some of the results contained in his joint paper with Ehresmann.
- This 1945 paper by Reeb also contains theorems about the existence or non-existence of compact integrals for exact Pfaffian forms and Reeb's next paper Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique Ⓣ(On the singular points of a completely integrable Pfaff form or numerical function) (1946) studied a certain type of singular point of a Pfaffian form.
- Reeb completed his doctoral thesis Propriétés topologiques des variétés feuilletées Ⓣ(Topological properties of laminated varieties) in 1948 and was awarded his doctorate.
- In 1952 Reeb was appointed to the University of Grenoble.
- Reeb gave a talk at the conference on Finsler and Cartan spaces.
- Reeb spent time at the Institute for Advanced Study at Princeton in 1954.
- In 1966 Reeb and Frenkel also founded the Institute de Recherche mathématique Avancée as the first university laboratory associated to the Centre National de la Recherche Scientifique.
- Frenkel was the first director of the Institute in 1966 but in the following year Reeb became director and held this position until Claude Godbillon took on that role in 1972.
- Another useful tool in topology was named after him, the "Reeb vector field" associated with a contact form.
- And Reeb's theorem is the one that tells you that, if a compact manifold has a function with only two critical points, this manifold is homeomorphic to a sphere.
- But Reeb did not care.
- Reeb published a number of books.
- The booklet was in three parts with the third part written by Reeb alone.
- In the summer of 1972, Reeb gave a lecture course at the University of Montreal in Canada.
- In his lectures, Reeb put into context the results which his very active trajectories research group in Strasbourg had obtained.
- Reeb found, and led others to find, not only knowledge and beauty in mathematics, but also virtue.
- Reeb was honoured many times for his outstanding contributions.
- That is what Reeb was for me, as certainly for many others, one of those beings who believe in the wisdom and goodness of man.
Born 12 November 1920, Saverne, Bas-Rhin, France. Died 6 November 1993, Strasbourg, France.
View full biography at MacTutor
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive