Detlef Gromoll

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

Life

Gromoll received his doctorate in 1964 under Friedrich Hirzebruch at the University of Bonn (Differentiable structures and metrics of positive curvature on spheres, Mathematical Annals 1966). He then went to the Universities of Mainz , Princeton University , the University of California, Berkeley (as Miller Fellow 1966/67) and Bonn before going to the State University of New York at Stony Brook in 1969 , where he became a professor. He was visiting professor at the Institut des Hautes Études Scientifiques (IHES), at the École polytechnique , of the Westphalian Wilhelms University in Münster (1983), inRio de Janeiro at IMPA (1984, 1996, 1997) and the Mathematical Sciences Research Institute (MSRI, 1993). He died of a brain haemorrhage.

Gromoll dealt with global aspects (properties "on a large scale") of Riemannian geometry , where he is known for a number of theorems. In 1972 he and Jeff Cheeger proved the " Soul Theorem " which was used in Perelman's proof for the Poincaré conjecture . The theorem says that a non-compact (i.e. infinitely extended), complete , non-negatively curved, n-dimensional Riemannian manifold M contains a compact , total geodetic , totally convex submanifold S (called "soul" of M by Gromoll, hence the name Soul Theorem), and that M is diffeomorphic to the normal bundle of S. If M has a strictly positive section curvature especially at every point, it is even diffeomorphic to the n-dimensional Euclidean space .

Previously, with Cheeger, he had classified the complete, non-compact Riemannian manifolds with positive section curvature. With Cheeger in 1972 he also proved the decomposition theorem for manifolds with non-negative Ricci curvature that contain a “straight line”. Together with Wolfgang Meyer he gave existence theorems for closed geodetic curves on compact Riemann manifolds ( theorem of Gromoll-Meyer ).

In 1970 he was invited speaker at the International Congress of Mathematicians (Manifolds of nonnegative curvature).

He had been married since 1971 and had three children.

Fonts

See also

Web links

Remarks

  1. ^ Cheeger, Gromoll: On the structure of complete manifolds of non-negative curvature. In: Annals of Mathematics. Series 2, Vol. 96, No. 3, 1972, pp. 413-443.
  2. ↑ sectional curvature (curvature Sectional) K is greater than or equal to zero.
  3. ↑ all geodetic curves of S are also those of M.
  4. ↑ Jeff Cheeger, Detlef Gromoll: The structure of complete manifolds of non-negative curvature. In: Bulletin American Mathematical Society. Vol. 74, No. 6, 1968, pp. 1147-1150, doi : 10.1090 / S0002-9904-1968-12088-9 .
  5. ^ Gromoll, Meyer: Periodic geodesics on compact Riemannian Manifolds. In: Journal of Differential Geometry. Vol. 3, No. 3/4, 1969, pp. 493-510.
personal data
SURNAME Gromoll, Detlef
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH May 13, 1938
PLACE OF BIRTH Berlin
DATE OF DEATH May 31, 2008
Place of death Stony Brook