Eugenio Calabi

Calabi was a Putnam Fellow as an undergraduate at the Massachusetts Institute of Technology in 1946. He received his Ph.D. in mathematics from Princeton University in 1950 after completing a doctoral dissertation, titled "Isometric complex analytic imbedding of Kahler manifolds", under the supervision of Salomon Bochner.[2] 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 Steele Prize from the American Mathematical Society 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.[3]

His work on the Calabi conjecture for Kähler metrics led to the development of Calabi–Yau manifolds; these, and the study of constant scalar curvature Kähler metrics and extremal Kähler metrics introduced by him in 1982 are central topics in complex differential geometry.

• Calabi, Eugenio. Isometric imbedding of complex manifolds. Ann. of Math. (2) 58 (1953), 1–23.
• Calabi, E. An extension of E. Hopf's maximum principle with an application to Riemannian geometry. Duke Math. J. 25 (1958), 45–56.
• Calabi, Eugenio. Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens. Michigan Math. J. 5 (1958), 105–126.
• Calabi, Eugenio. Minimal immersions of surfaces in Euclidean spheres. J. Differential Geometry 1 (1967), 111–125.
• Calabi, Eugenio. Examples of Bernstein problems for some nonlinear equations. 1970 Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968) pp. 223–230 Amer. Math. Soc., Providence, R.I.
• Calabi, E. Métriques kählériennes et fibrés holomorphes. (French) [Kähler metrics and holomorphic vector bundles] Ann. Sci. École Norm. Sup. (4) 12 (1979), no. 2, 269–294.
• Calabi, Eugenio. Extremal Kähler metrics. Seminar on Differential Geometry, pp. 259–290, Ann. of Math. Stud., 102, Princeton Univ. Press, Princeton, N.J., 1982.
• Calabi, Eugenio. Extremal Kähler metrics. II. Differential geometry and complex analysis, 95–114, Springer, Berlin, 1985.

• Calabi triangle
• Calabi flow
• Calabi–Yau algebra
• Calabi–Eckmann manifold
• Shing-Tung Yau (born 1949), a Chinese-born American mathematician awarded the Fields Medal in 1982
• Erich Kähler (1906–2000), a German mathematician