German mathematician
Wilhelm Paul Albert Klingenberg (28 January 1924 – 14 October 2010) was a German mathematician who worked on differential geometry and in particular on closed geodesics .
Life
Klingenberg was born in 1924 as the son of a Protestant minister. In 1934 the family moved to Berlin ; he joined the Wehrmacht in 1941. After the war, he studied mathematics at the University of Kiel , where he finished his Ph.D. in 1950 with Karl-Heinrich Weise , with a thesis in affine differential geometry .
After some time as an assistant of Friedrich Bachmann , he worked in the group of Wilhelm Blaschke at the University of Hamburg , where he defended his Habilitation in 1954. He then visited Sapienza University of Rome , working in the group of Francesco Severi and Beniamino Segre , after which he obtained a faculty position at the University of Göttingen (with Kurt Reidemeister ), where he stayed until 1963.
In 1954–55 Klingenberg spent a year at Indiana University Bloomington ; during this time he also visited Marston Morse at Princeton University . In 1956–58 he accepted invitations to the Institute for Advanced Study in Princeton, New Jersey . In 1962 he visited the University of California, Berkeley as a guest of Shiing-Shen Chern , who he knew from his time in Hamburg. Later he became a full (C4-) professor at the University of Mainz , and in 1966 a full (C4-) professor at the University of Bonn , a position he kept till his retirement in 1989.
Klingenberg married Christine Klingenberg née Kob in 1953 and has two sons and a daughter.
In 1966 he was an invited speaker at the quadrennial International Congress of Mathematicians in Moscow ; his talk was on "Morse theory in the space of closed curves".
Work
Klingenberg's area of work was geometry, especially differential geometry and Riemannian geometry . Besides many articles he published several books. One of his major achievements was the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a complete , simply connected Riemannian manifold with sectional curvature contained in the interval (1, 4] is homeomorphic to the sphere .
Publications
Gromoll, Detlef ; Klingenberg, Wilhelm; Meyer, Wolfgang (1968). Riemannsche Geometrie im Grossen . Lecture Notes in Mathematics. Vol. 55. Berlin-New York: Springer Verlag. MR 0229177 .
Klingenberg, Wilhelm (1978), A course in differential geometry , Berlin, New York: Springer-Verlag , ISBN 978-0-387-90255-5 , MR 0474045
Klingenberg, Wilhelm (1978), Lectures on closed geodesics , Grundlehren der Mathematischen Wissenschaften, vol. 230, Berlin, New York: Springer-Verlag , ISBN 978-3-540-08393-1 , MR 0478069 [ 1]
Klingenberg, Wilhelm (1982), Riemannian geometry , de Gruyter Studies in Mathematics, vol. 1, Berlin: Walter de Gruyter & Co., ISBN 978-3-11-008673-7 , MR 0666697 [ 2]
Klingenberg, Wilhelm P. A. (1991), Selected papers , Series in Pure Mathematics, vol. 14, River Edge, NJ: World Scientific Publishing Co. Inc., ISBN 978-981-02-0764-9 , MR 1148072
See also
References
External links
International National Academics People Other