Richard Lawrence Bishop is an American mathematician , Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign [1] . The most famous Bishop's inequality - Gromov , named in his honor, together with Gromov .
| Richard Lawrence Bishop | |
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| English Richard L. Bishop | |
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| Site | math.uiuc.edu/~bishop/ |
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Biography
Richard Bishop studied at Case Western Reserve University . He received a bachelor's degree in 1954. He defended his thesis at the Massachusetts Institute of Technology in 1959 under the leadership of Isadore Singer [2] .
After that, he began working at the University of Illinois at Urbana-Champaign , now an honorary professor .
He also had temporary positions at the University of California at Los Angeles and the Massachusetts Institute of Technology .
Scientific contribution
He proved a particular case of the so-called Bishop-Gromov inequality . It was generalized by Gromov and is a key tool in the study of Riemannian manifolds with a bounded Ricci curvature .
Together with Stephanie Alexander, he presented the necessary and sufficient conditions for curved products with curvature bounded below and above in the sense of Aleksandrov . A generalization of the Cartan-Hadamard theorem was also obtained with it.
Books
- Bishop RL, Crittenden RJ Geometry of Manifolds. - Academic Press, 1964. , second edition of AMS-Chelsea, 2000.
- translated into Russian by Bishop RL, Crittenden RJ. Geometry of varieties. - 1967 ..
- Bishop RL, Goldberg SI Tensor Analysis on Manifolds. - 1968 .
Links
- ↑ Emeritus faculty Archival copy of July 14, 2014 at Wayback Machine , UIUC Mathematics, retrieved 2014-06-16.
- ↑ Richard Lawrence Bishop at the Mathematics Genealogy Project