Wilhelm Paul Albert Klingenberg

Quick Info

28 January 1924
Rostock, Mecklenburg, Germany
14 October 2010
Röttgen, Bonn, Germany

Wilhelm Klingenberg was a German mathematician who worked on differential geometry.


Wilhelm Klingenberg's parents were Paul Klingenberg, a Protestant Minister, and Henny Dunker. Wilhelm was the oldest of his parents' six children. The family moved to Berlin in 1934, partly because there were better schools in Berlin and partly because Paul Klingenberg had joined the Bekennende Kirche, an organisation set up to oppose the Nazi Party's efforts to Nazify the Protestant Church. Wilhelm attended schools in Berlin where he learnt Latin, Greek and French but he had to study mathematics on his own. He entered the Joachimsthalsces Gymnasium in 1937 and received his school diploma in 1941. He applied to enter the University of Berlin but this was not permitted and he had to serve in the army. He writes in [1]:-
When the end of the war finally gave me my freedom, I changed my handwriting and started looking for a place to study. The devastated and Soviet occupied city of Berlin was out of the question, Göttingen and Hamburg were filled up, so I went to Kiel University.
Klingenberg obtained a doctorate in 1950 with a thesis on affine differential geometry. from 1950 to 1952 he was a research assistant at Kiel where F Bachmann interested him in the foundations of geometry. At this time he solved a problem on equivalences of configurations in an affine plane which Ruth Moufang had worked on. Blaschke advised him regarding trips to Italy and he spent time in 1952/53 at the University of Rome where he was strongly influenced by F Severi, E Bompiani and Beniamino Segre.

After returning to Germany he completed his habilitation thesis at Hamburg and then obtained a permanent position at Göttingen working with Reidemeister. He wrote in [1]:-
I have fond memories of our years there - Reidemeister had a brilliant mind and a wide range of interests, his wife Elisabeth was a renowned photographer.
Klingenberg spent 1954/55 at Bloomington in the United States visiting Morse at Princeton during his time at Bloomington. His interests had turned away from affine and projective differential geometry and turned towards Riemannian geometry. Although he remained on the staff at Göttingen until 1963, Klingenberg spent 1956/57 and 1957/58 at the Institute for Advanced Study at Princeton. He also spent 1962 at the University of California at Berkeley at the invitation of S S Chern. Klingenberg wrote in [1]:-
I had met him in Hamburg in 1953 when he visited his former teacher Blaschke, and since that time he had actively helped my career whenever he had a chance to do so.
While at Berkeley, Klingenberg received offers of chairs at Würzburg and Mainz - he chose Mainz. Three years later, in 1966, he was offered chairs at Zürich and at Bonn. He chose, not without some difficulty, to accept the offer from Bonn. However Bonn grew rapidly with additional staff and students:-
... and some of the intimate charm of a close-knit group thereby went down the drain. Not without some pain and struggle, I finally accepted the change and concentrated my activities on my own differential geometry group.
Klingenberg worked during his years at Bonn on closed geodesics. He retired in 1989. His major books include A course in differential geometry (1978), Lectures on closed geodesics (1978) and Riemannian geometry (1982). Of this last work Klingenberg comments:-
It was the first book on this subject since the monograph of L P Eisenhart in 1926.
In 1953 Klingenberg married Christine Kob, they have two sons and a daughter.

Among the honours he has received, we mention his election to the Academy of Sciences and Literature in Mainz, and the award of an honorary doctorate by the University of Leipzig. He gives his hobbies as: piano, horse-back riding, Chinese art and the art of Albrecht Dürer. His interest in Chinese art led to him making trips to China and Tibet. This in turn led to his publication of the book Tibet - Erfahrungen auf dem Dach der Welt published first in 1997 and in a paperback version in 2001:-
Wilhelm Klingenberg knows Tibet like no other. Every year he travels to this mysterious country, visits famous monasteries and holy mountains, inaccessible meditation caves and lakes. He goes by the old pilgrim routes and knows the life of the yak herders. With each trip he became more and more under the spell of this unique civilization where the great edifice of Lamaism was built. ... [The book provides] an unusual blend of practical information and personal travel log ...

References (show)

  1. Wilhelm P A Klingenberg, Selected papers of Wilhelm P A Klingenberg (Singapore, 1991).

Additional Resources (show)

Other websites about Wilhelm Klingenberg:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry

Honours (show)

Honours awarded to Wilhelm Klingenberg

  1. BMC plenary speaker 1969

Written by J J O'Connor and E F Robertson
Last Update September 2009