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Eugenio Calabi
Summary
Eugenio Calabi (born 11 May 1923) is an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics, Emeritus, at the University of Pennsylvania, specializing in differential geometry, partial differential equations and their applications.
Calabi was a Putnam Fellow as an undergraduate at the Massachusetts Institute of Technology in 1946. He received his PhD in mathematics from Princeton University in 1950 after completing a doctoral dissertation, titled "Isometric complex analytic imbedding of Kähler manifolds", under the supervision of Salomon Bochner. He later obtained a professorship at the University of Minnesota.
In 1964, Calabi joined the mathematics faculty at the University of Pennsylvania. Following the retirement of the German-born American mathematician Hans Rademacher, he was appointed to the Thomas A. Scott Professorship of Mathematics at the University of Pennsylvania in 1967. He won the Leroy P. Steele Prize from the American Mathematical Society (AMS) in 1991 for his work in differential geometry. In 1994, Calabi assumed emeritus status. In 2012, he became a fellow of the American Mathematical Society. In 2021, he was awarded Commander of the Order of Merit of the Italian Republic.
He turned 100 on May 11, 2023.
Calabi has made a number of contributions to the field of differential geometry. Other contributions, not discussed here, include the construction of a holomorphic version of the long line with Maxwell Rosenlicht, a study of the moduli space of space forms, a characterization of when a metric can be found so that a given differential form is harmonic, and various works on affine geometry. In the comments on his collected works in 2021, Calabi cited his article Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens as that which he is "most proud of".
At the 1954 International Congress of Mathematicians, Calabi announced a theorem on how the Ricci curvature of a Kähler metric could be prescribed.
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In the mathematical field of differential geometry, Ricci-flatness is a condition on the curvature of a (pseudo-)Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental interest, as they are the solutions of Einstein's field equations in vacuum with vanishing cosmological constant. In Lorentzian geometry, a number of Ricci-flat metrics are known from works of Karl Schwarzschild, Roy Kerr, and Yvonne Choquet-Bruhat.
Shing-Tung Yau
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