Georges Reeb

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Georges Reeb (1970)

Georges Henri Reeb (born November 12, 1920 in Saverne in Alsace ; † November 6, 1993 in Strasbourg ; also Georg Henri Reeb ) was a French mathematician who dealt with differential topology and differential geometry , differential equations (topological theory of dynamic systems) and nonstandard analysis .

Reeb received his doctorate in 1943 from the University of Strasbourg under Charles Ehresmann ( Propriétés topologiques des variétés feuilletées ). He was a professor in Grenoble (Université Fourier) and Strasbourg (Université Louis Pasteur), where he was director of the Mathematical Institute (Institute de Recherche mathématique Avancée, IRMA) from 1967 to 1972, which he founded in 1966 with Jean Frenkel. Together with Jean Leray and Pierre Lelong, both founded a series of meetings between theoretical physicists and mathematicians in Strasbourg in 1965 (Rencontres entre Mathématiciens et Physiciens Théoriciens). In 1954 he was at the Institute for Advanced Study .

Reeb is the founder of the topological theory of Foliations (Foliations, feuilletées) manifolds with a special local product structure. The Reeb foliation is a foliation of the 3-sphere with leaves diffeomorphic to and one leaf out of a compact 2-torus. Reeb's stability theorem describes leaves that have a compact leaf of finite holonomy: in this case, in a neighborhood of this leaf, all leaves are compact and have finite holonomy.

Reeb's theorem in Morse's theory says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. The Reeb vector field in contact geometry is named after him.

Reeb was an honorary doctorate from the Albert Ludwig University of Freiburg . In 1967 he was President of the Société Mathématique de France .

Georges Reeb (right) with Jean-Pierre Serre (3rd from left), René Thom (left) and others in Oberwolfach in 1949

See also

Works (selection)

  • Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique. CR Acad. Sci. Paris 222, (1946). 847-849.
  • Variétés feuilletées, feuilles voisines. CR Acad. Sci. Paris 224, (1947). 1613-1614.
  • Sur certaines propriétés topologiques des variétés feuilletées. Publ. Inst. Math. Univ. Strasbourg 11, pp. 5-89, 155-156. Actualités Sci. Ind., No. 1183 Hermann & Cie., Paris, 1952.
  • with André Haefliger : Variétés (non séparées) à une dimension et structures feuilletées du plan. Enseignement Math. (2) 3 (1957), 107-125.

Web links

personal data
SURNAME Reeb, Georges
ALTERNATIVE NAMES Reeb, Georges Henri (full name); Reeb, Georg Henri
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH November 12, 1920
PLACE OF BIRTH Saverne
DATE OF DEATH November 6, 1993
Place of death Strasbourg