Warren Ambrose

Arthur Warren Ambrose ( born October 25, 1914 in Virden, Illinois, † December 4, 1995 in Paris) was an American mathematician who dealt with differential geometry.

Life

Ambrose studied mathematics at the University of Illinois at Urbana -Champaign with a bachelor 's degree in 1935, her Master's degree in 1936 and his doctorate at Joseph L. Doob 1939 ( Some properties of measurable stochastic processes ). After that, he was at the University of Alabama, the Institute for Advanced Study and Princeton University, the University of Michigan and Yale University. In 1947, he was Assistant Professor, 1950 Associate Professor and in 1957 Professor at the Massachusetts Institute of Technology. With Isadore M. Singer he made the MIT in the 1950s to one of the centers of differential geometry in the U.S. ( in addition to Chicago, where SS Chern was then). In 1985, he retired.

He was repeatedly at the Institute for Advanced Study ( 1939-1941, 1948/49, 1959), and Visiting Professor in Latin America, Italy, India, Belgium. In 1954, he conducted research for the United States Air Force in Brussels and Paris.

In the 1960s, he was a visiting professor in Buenos Aires (where he was a visiting professor in Brazil and Buenos Aires first 1948). After 1966, other faculty members and students at the University of Buenos Aires abused by military police (after a coup, the military had the universities occupied ) was, he was a staunch opponent of the right-wing military dictatorships in Latin America and especially in Argentina and Chile. He also took many students from Buenos Aires to MIT. Also in the 1960s he was active in the protest against the U.S. involvement in the Vietnam War and wrote in 1967 a relevant call for tax boycott.

Work

Initially, he was concerned with stochastic processes ( the subject of his dissertation at Doob ), then with ergodic theory and measure theory ( which he published with Paul Halmos and Shizuo Kakutani ).

The set of Ambrose and Singer connects the curvature form of the holonomy of the connection form in a principal fiber bundle (clearly the Krümungstensor supplies applied to a tangent, the difference in parallel transport of the tangent vector to infinitesimal closed paths ).

He is known for the set of Cartan - Ambrose - Hicks (1956, named additionally after his doctoral Noel Hicks ), which answers the question of the extent of the Riemann curvature tensor determines the Riemannian metric. The local problem had already been solved Elie Cartan. The global problem of determining metrics of parallel transport and curvature is also known as Ambrose problem.

Honors, Private

1948/49, he was a Guggenheim Fellow.

He was married twice and had two children from his first marriage. In his second marriage he was married to a French woman, with whom he moved to his retirement in 1989 after France.

He was fluent in French, Portuguese and Spanish, was a wine lover and jazz fan ( Charlie Parker).

Writings

• With Singer A theorem on holonomy, Trans Amer. Math Soc., Volume 75, 1953, pp. 428-443
• Parallel translation of Riemannian curvature, Annals of Mathematics, Volume 64, 1956, pp. 337-363
• On homogeneous Riemannian manifolds with Singer, Duke Math J., Volume 25, 1958, pp. 647-669