Detlef Gromoll

Detlef Gromoll ( born May 13, 1938 in Berlin, † 31 May, 2008 Stony Brook ) was a German mathematician who worked on differential geometry.

Gromoll his doctorate in 1964 at Friedrich Hirzebruch at Bonn University ( Differentiable structures and metrics of positive curvature on spheres, Annals of Mathematics 1966). After that, he was at the University of Mainz, Princeton University, the University of California, Berkeley ( as a Miller Fellow 1966/67 ) and Bonn before he went in 1969 to the State University of New York at Stony Brook, where he became a professor. He was a visiting professor at the Institut des Hautes Études Scientifiques ( IHES ), at the Ecole Polytechnique, the Westfälische Wilhelms- University in Münster (1983 ), in Rio de Janeiro on IMPA (1984, 1996, 1997 ) and at the Mathematical Sciences Research Institute ( MSRI, 1993). He died of a brain hemorrhage.

Gromoll concerned with global aspects ( properties " in the large" ) of Riemannian geometry, where he is known for a number of theorems. In 1972 he proved with Jeff Cheeger, the "Soul Theorem", which was used in the proof of Perelman's for the Poincaré conjecture. The theorem states that a non-compact (ie infinitely extended ), complete, non- negatively curved n-dimensional Riemannian manifold M contains a compact, totally geodesic, totally convex submanifold S (of Gromoll called "soul" of M, therefore the name Soul theorem), and that M is diffeomorphic to the normal bundle of fibers of S. If M has specially at any point a strictly positive sectional curvature, it is even diffeomorphic to the n- dimensional Euclidean space.

He had previously classified with the Cheeger complete, non- compact Riemannian manifolds with positive sectional curvature. With Cheeger he proved in 1972 the splitting theorem on manifolds with nonnegative Ricci curvature, the " straight line" included a. He was also with Wolfgang Meyer existence theorems for closed geodesics on compact Riemann manifolds curves.

It was in 1970 Invited Speaker at the International Congress of Mathematicians ( Manifolds of Nonnegative curvature ).

He was married in 1971 and had three children.

Writings

  • With Gerard Walschap: Metric foliations and curvature. Birkhäuser 2008
  • Wilhelm Klingenberg, Wolfgang Meyer: Riemannian geometry in the large. Springer 1968, 2nd edition 1975
  • With W. Meyer: Periodic geodesics on compact riemannian manifolds. J. Differential Geometry 3 1969 493-510.
  • With J. Cheeger: The splitting theorem for manifolds of Nonnegative Ricci curvature. J. Differential Geometry 6 (1971 /72), 119-128.
  • With J. Cheeger: On the structure of complete manifolds of Nonnegative curvature. Ann. of Math ( 2) 96 (1972 ), 413-443.
  • With W. Meyer: An exotic sphere with Nonnegative sectional curvature. Ann. of Math (2 ) 100 ( 1974), 401-406.
  • With U. Abresch: On complete manifolds with Nonnegative Ricci curvature. J. Amer. Math Soc. 3 (1990 ), no 2, 355-374.
May 31 Stony Brook, New York Stony Brook University Instituto Nacional de Matemática Pura e Aplicada Integrated Authority File
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