Wilhelm Paul Albert Klingenberg , a German mathematician, one of the founders of the modern school of differential geometry in Germany, is best known for his results on closed geodesics and the sphere theorem , which was proved together with Marcel Berger in 1960.
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Life
Wilhelm Klingenberg was born in 1924 in the family of a Protestant pastor in Rostock . In 1934, the family moved to Berlin . He served in the army since 1941.
After the war, he studied mathematics in Kiel, where he received his doctorate in 1950 under the direction of in affine differential geometry . Soon he worked as an assistant to Friedrich Bachmann and began working in the Wilhelm Blaschke group in Hamburg. Here he defended habilitation in 1954. He also worked in Rome in a group with Francesco Severi and Benyamino Segre . He got a position at the University of Gottingen , where he remained until 1963.
In 1954-1955, he worked at Indiana University in Bloomington . During this time, he also visited Morse at Princeton . In 1956-1958 he was a visiting professor at the Institute for Advanced Study at Princeton University. In 1962, he visited the University of California at Berkeley as a guest of Chen , whom he had known since his time in Hamburg. Later he became a full professor at the Johannes Gutenberg University of Mainz , and in 1966 he became a full professor at the University of Bonn . In this position, he worked until his retirement in 1989.
Klingenberg married in 1953 Christine Klingenberg (née Kob), has two sons and a daughter.
Recognition
In 1966, he was a guest speaker at the International Congress of Mathematicians in Moscow. There he read a report on the topic "Morse theory on the space of closed curves") [3] .
Publications
- In Russian
- Gromol D., Klingenberg V., Meyer V. Rimanova geometry as a whole. - World, 1971.
- Klingenberg V. Lectures on closed geodesics. - World, 1982.
- On memetsky
- Gromoll, D .; Klingenberg, W .; Meyer, W. Riemannsche Geometrie im Grossen. - Berlin-New York, 1968 .-- vi + 287 p. - (Lecture Notes in Mathematics No. 55).
- In English
- Klingenberg, Wilhelm (1978), A course in differential geometry , Berlin, New York: Springer-Verlag , ISBN 978-0-387-90255-5 , < https://books.google.com/books?id=8F7vAAAAMAAJ >
- Klingenberg, Wilhelm (1978), Lectures on closed geodesics , vol. 230, Grundlehren der Mathematischen Wissenschaften, Berlin, New York: Springer-Verlag , ISBN 978-3-540-08393-1 , < https://books.google.com/books?id=HkmhUkJj3pUC&pg=PA122 > [four]
- Klingenberg, Wilhelm (1982), Riemannian geometry , vol. 1, de Gruyter Studies in Mathematics, Berlin: Walter de Gruyter & Co., ISBN 978-3-11-008673-7 , < https://books.google.com/books?id=wscVZ-RrCpMC > [five]
- Klingenberg, Wilhelm PA (1991), Selected papers , vol. 14, Series in Pure Mathematics, River Edge, NJ: World Scientific Publishing Co. Inc., ISBN 978-981-02-0764-9 , < https://books.google.com/books?id=qXexLXz9mvEC >
Links
- ↑ 1 2 Archive for the history of mathematics MacTyutor
- ↑ Mathematical Genealogy - 1997.
- ↑ Archived copy (inaccessible link) . Date of treatment November 19, 2016. Archived September 23, 2016.
- ↑ Green, Leon. Review: Lectures on closed geodesics , by W. Klingenberg (Eng.) // Bull. Amer. Math. Soc. (NS) : journal. - 1979. - Vol. 1 , no. 3 . - P. 568-570 . - DOI : 10.1090 / s0273-0979-1979-14626-3 .
- ↑ Greene, Robert E. Review: Riemannian geometry , by W. Klingenberg (Eng.) // Bull. Amer. Math. Soc. (NS) : journal. - 1984. - Vol. 11 , no. 1 . - P. 193-197 . - DOI : 10.1090 / s0273-0979-1984-15266-2 .