Manfredo Perdigão do Carmo (15 August 1928, Maceió – 30 April 2018, Rio de Janeiro) was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.[1]
Manfredo do Carmo | |
|---|---|
.jpg) do Carmo in 1979 | |
| Born | 15 August 1928 |
| Died | 30 April 2018 (aged 89) |
| Resting place | Cemitério de São João Batista |
| Nationality | Brazilian |
| Alma mater | University of California, Berkeley |
| Awards | Guggenheim Fellowship (1965, 1968) Prêmio Almirante Álavaro Alberto (1984) Brazil's National Order of Scientific Merit (1995) TWAS Prize (1987) AMS Fellow (2012) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Instituto Nacional de Matemática Pura e Aplicada |
| Thesis | The Cohomology Ring of Certain Kahlerian Manifolds (1963) |
| Doctoral advisor | Shiing-Shen Chern |
| Doctoral students | Celso Costa Marcos Dajczer Keti Tenenblat |
Education and career
Do Carmo studied civil engineering at the University of Recife from 1947 to 1951. After working a few years as engineer, he accepted a teaching position at the newly created Institute of Physics and Mathematics at Recife.[2]
On suggestion of Elon Lima, in 1959 he went to Instituto Nacional de Matemática Pura e Aplicada to improve his background[2][3] and in 1960 he moved to the US to pursue a Ph.D. in mathematics at the University of California, Berkeley under the supervision of Shiing-Shen Chern. He defended his thesis, entitled "The Cohomology Ring of Certain Kahlerian Manifolds", in 1963.[4]
After working again at University of Recife and at the University of Brasilia, in 1966 he became professor at Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. From 2003 to his death he was emeritus professor at the same institution.[2]
Do Carmo was a Guggenheim Fellow in 1965 and 1968.[5][6] In 1978 he was invited speaker at the International Congress of Mathematicians held in Helsinki.[7][8][9] In 1991 he obtained a Doctorate honoris causa from Federal University of Alagoas[10][11] and in 2012 from University of Murcia[12][13] and from Federal University of Amazonas.[14][15]
He served as president of the Brazilian Mathematical Society in the term 1971–1973.[16] He was elected a member of the Brazilian Academy of Sciences in 1970,[17] a member of The World Academy of Sciences (TWAS) in 1997[18] and a fellow of the American Mathematical Society In 2013.[19]
Among his awards, he received the Prêmio Almirante Álavaro Alberto from the National Council for Scientific and Technological Development in 1984,[20] the TWAS Prize in Mathematics in 1992,[18][21] the National Order of Scientific Merit in 1995[22] and the Comenda Graciliano Ramos from the municipality of Maceió in 2000.
Do Carmo died on 30 April 2018 at the age of 89.[23][24][25]
Research
Do Carmo's main research interests were Riemannian geometry and the differential geometry of surfaces.[3]
In particular, he worked on rigidity and convexity of isometric immersions,[26][27] stability of hypersurfaces[28][29] and of minimal surfaces,[30][31] topology of manifolds,[32] isoperimetric problems,[33] minimal submanifolds of a sphere,[34][35] and manifolds of constant mean curvature[36][37][38][39] and vanishing scalar curvature.[40]
Do Carmo published more than 100 papers in peer-reviewed journals;[41] in 2012 a selection of his works was published by Springer.[42] He is also known for his textbooks:[43][44] they were translated into many languages and used in courses from universities such as Harvard and Columbia.[45][2]
He supervised 27 PhD students, including Celso Costa, Marcos Dajczer and Keti Tenenblat.[4]
Books
- Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976 ISBN 9780132125895.[46]
- Riemannian Geometry, Birkhäuser, 1992 ISBN 978-0-8176-3490-2
- Differential Forms and Applications, Springer Verlag, Universitext, 1994 ISBN 978-3-540-57618-1
- (with Eduardo Wagner and Augusto Cezar de Oliveira Morgado). Trigonometria – Números Complexos ISBN 8583370168