Detlef Gromoll
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
- with Wilhelm Klingenberg , Wolfgang Meyer : Riemannsche Geometrie im Großes (= Lecture Notes in Mathematics . 55). Springer, Berlin et al. 1968, (2nd edition. Ibid 1975, ISBN 3-540-07133-4 ).
- with Wolfgang Meyer: Periodic geodesics on compact riemannian manifolds. In: Journal of Differential Geometry . Vol. 3, No. 3/4, 1969, pp. 493-510, doi : 10.4310 / jdg / 1214429070 .
- with Jeff Cheeger : The splitting theorem for manifolds of nonnegative Ricci curvature. In: Journal of Differential Geometry. Vol. 6, No. 1, 1971, pp. 119-128, doi : 10.4310 / jdg / 1214430220 .
- with Jeff Cheeger: On the structure of complete manifolds of nonnegative curvature. In: Annals of Mathematics . Serie 2, Vol. 96, No. 3, 1972, pp. 413-443, doi : 10.2307 / 1970819 .
- with Wolfgang Meyer: An exotic sphere with non-negative sectional curvature. In: Annals of Mathematics. Series 2, Vol. 100, No. 3, 1974, pp. 401-406, doi : 10.2307 / 1971078 .
- with Uwe Abresch: On complete manifolds with non-negative Ricci curvature. In: Journal of the American Mathematical Society . Vol. 3, No. 2, 1990, pp. 355-374, doi : 10.2307 / 1990957 .
- with Gerard Walschap : Metric foliations and curvature (= Progress in Mathematics. 403). Birkhäuser, Basel et al. 2009, ISBN 978-3-7643-8714-3 .
See also
Web links
- Kenneth Chang: Detlef Gromoll, Known for Math 'Soul' Idea, Dies at 70. In: New York Times , June 19, 2008 (English).
- John J. O'Connor, Edmund F. Robertson : Detlef Gromoll. In: MacTutor History of Mathematics archive .
Remarks
- ^ 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.
- ↑ sectional curvature (curvature Sectional) K is greater than or equal to zero.
- ↑ all geodetic curves of S are also those of M.
- ↑ 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 .
- ^ Gromoll, Meyer: Periodic geodesics on compact Riemannian Manifolds. In: Journal of Differential Geometry. Vol. 3, No. 3/4, 1969, pp. 493-510.
personal data | |
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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 |