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]

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]

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]

• 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