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 | |
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![]() do Carmo in 1979 | |
Born | |
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
editDo 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]
Forschung
editDo 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
edit- 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
References
edit- ^ Gorodski, Claudio; Piccione, Paolo (2021-06-01). "Opening note: An homage to Manfredo P. do Carmo". São Paulo Journal of Mathematical Sciences. 15 (1): 1–2. doi:10.1007/s40863-020-00194-0. ISSN 2316-9028. S2CID 228984989.
- ^ a b c d Queiroz, Antonio José Melo de (2020). "O percurso profissional de Manfredo Perdigão do Carmo e a geometria differencial no Brasil" [The professional path of Manfredo Perdigão do Carmo and differential geometry in Brazil]. Boletim Cearense de Educação e História da Matemática (in Portuguese). 7 (20): 266–276. doi:10.30938/bocehm.v7i20.2819. ISSN 2447-8504. S2CID 225625329.
- ^ a b Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti (eds.), "A Summary of the Scientific Activities", Manfredo P. do Carmo – Selected Papers, Berlin, Heidelberg: Springer, pp. 1–5, doi:10.1007/978-3-642-25588-5_1, ISBN 978-3-642-25588-5, retrieved 2022-01-31
- ^ a b Manfredo do Carmo at the Mathematics Genealogy Project
- ^ Biography from the Guggenheim Foundation
- ^ "John Simon Guggenheim Foundation | Manfredo Perdigao do Carmo". Retrieved 2022-01-31.
- ^ Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Helsinki. p. 401.
{{cite book}}
: CS1 maint: location missing publisher (link) - ^ do Carmo, Manfredo P. (1980), "Minimal surfaces: stability and finiteness", Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, pp. 401–405, MR 0562633.
- ^ Carmo, Manfredo P. do (2012), do Carmo, Manfredo P.; Tenenblat, Keti (eds.), "Minimal Surfaces: Stability and Finiteness", Manfredo P. do Carmo – Selected Papers, Berlin, Heidelberg: Springer, pp. 139–143, doi:10.1007/978-3-642-25588-5_12, ISBN 978-3-642-25588-5, retrieved 2022-02-01
- ^ "Ufal promove evento internacional na área de Matemática" [Ufal promotes international event in an area of mathematics]. Universidade Federal de Alagoas (in Brazilian Portuguese). Retrieved 2022-02-07.
- ^ "Alagoano referência em geometria diferencial será homenageado em evento" [Alagoan reference in differential geometry will be homaged in an event]. Universidade Federal de Alagoas (in Brazilian Portuguese). Retrieved 2022-02-07.
- ^ "Professor Manfredo P. Do Carmo will be awarded the honorary degree Doctor Honoris Causa by the Universidad de Murcia | European Mathematical Society". euro-math-soc.eu. Retrieved 2022-02-01.
- ^ Laudatio del Padrino (in Spanish), 2012-05-15, retrieved 2022-02-06
- ^ "Ata da sessão solene de outorga de titulo Dr. Honoris Causa" [Acts of the solemn session to grant the title of Dr. Honoris Causa] (PDF) (in Portuguese).
- ^ "Resolução N° 009/2012" (PDF) (in Portuguese).
- ^ "Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática" (in Brazilian Portuguese). Retrieved 2022-01-31.
- ^ "Manfredo Perdigão do Carmo – ABC" (in Brazilian Portuguese). Retrieved 2022-01-31.
- ^ a b "do Carmo, Manfredo P." TWAS. Retrieved 2022-01-31.
- ^ List of Fellows of the American Mathematical Society, retrieved 2015-01-13.
- ^ "CNPq - Prêmio Almirante Álvaro Alberto". www.premioalvaroalberto.cnpq.br (in Portuguese). Retrieved 2022-02-01.
- ^ "Prizes and Awards". The World Academy of Sciences. 2016.
- ^ "Ordem Nacional do Mérito Científico" (in Portuguese). Instituto Brasileiro de Informação em Ciência e Tecnologia . 11 August 2023.
- ^ "Matemático Manfredo do Carmo morre aos 89 anos" [Mathematician Manfredo do Carmo dies at age 89] (in Portuguese). IMPA. Retrieved 1 May 2018.
- ^ "Decease of Prof. Do Carmo | European Mathematical Society". euro-math-soc.eu. Retrieved 2022-01-31.
- ^ "News from the AMS". American Mathematical Society. Retrieved 2022-01-31.
- ^ do Carmo, M. P.; Warner, F. W. (1970). "Rigidity and convexity of hypersurfaces in spheres". Journal of Differential Geometry. 4 (2). doi:10.4310/jdg/1214429378. ISSN 0022-040X.
- ^ doCarmo, Manfredo P.; Lima, Elon (1969-05-01). "Isometric immersions with semi-definite second quadratic forms". Archiv der Mathematik. 20 (2): 173–175. doi:10.1007/BF01899010. ISSN 1420-8938. S2CID 189777457.
- ^ Barbosa, João Lucas; do Carmo, Manfredo (1984-09-01). "Stability of hypersurfaces with constant mean curvature". Mathematische Zeitschrift. 185 (3): 339–353. doi:10.1007/BF01215045. ISSN 1432-1823. S2CID 186222313.
- ^ Barbosa, J. Lucas; do Carmo, Manfredo; Eschenburg, Jost (1988-03-01). "Stability of hypersurfaces of constant mean curvature in Riemannian manifolds". Mathematische Zeitschrift. 197 (1): 123–138. doi:10.1007/BF01161634. ISSN 1432-1823. S2CID 186231004.
- ^ Barbosa, J. L.; Carmo, M. Do (1976). "On the Size of a Stable Minimal Surface in R3". American Journal of Mathematics. 98 (2): 515–528. doi:10.2307/2373899. ISSN 0002-9327. JSTOR 2373899.
- ^ do Carmo, M.; Peng, C. K. (1979). "Stable complete minimal surfaces in 𝑅³ are planes". Bulletin of the American Mathematical Society. 1 (6): 903–906. doi:10.1090/S0273-0979-1979-14689-5. ISSN 0273-0979.
- ^ do Carmo, Manfredo; Xia, Changyu (2000-02-01). "Ricci curvature and the topology of open manifolds". Mathematische Annalen. 316 (2): 391–400. doi:10.1007/s002080050018. ISSN 1432-1807. S2CID 189881132.
- ^ Barbosa, João Lucas; Carmo, Manfredo do (1978-10-01). "A proof of a general isoperimetric inequality for surfaces". Mathematische Zeitschrift. 162 (3): 245–261. doi:10.1007/BF01186367. ISSN 1432-1823. S2CID 186236970.
- ^ Chern, S. S.; do Carmo, M.; Kobayashi, S. (1970), Browder, Felix E. (ed.), "Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length", Functional Analysis and Related Fields: Proceedings of a Conference in honor of Professor Marshall Stone, held at the University of Chicago, May 1968, Berlin, Heidelberg: Springer, pp. 59–75, doi:10.1007/978-3-642-48272-4_2, ISBN 978-3-642-48272-4, retrieved 2022-02-01
- ^ Carmo, Manfredo P. Do; Wallach, Nolan R. (1971). "Minimal Immersions of Spheres into Spheres". Annals of Mathematics. 93 (1): 43–62. doi:10.2307/1970752. ISSN 0003-486X. JSTOR 1970752.
- ^ do Carmo, Manfredo P.; Dajczer, Marcos (1982-01-01). "Helicoidal surfaces with constant mean curvature". Tohoku Mathematical Journal. 34 (3). doi:10.2748/tmj/1178229204. ISSN 0040-8735. S2CID 109931575.
- ^ Carmo, M. Do; Dajczer, M. (1983). "Rotation Hypersurfaces in Spaces of Constant Curvature". Transactions of the American Mathematical Society. 277 (2): 685–709. doi:10.2307/1999231. ISSN 0002-9947. JSTOR 1999231.
- ^ Alencar, Hilário; do Carmo, Manfredo (1994). "Hypersurfaces with constant mean curvature in spheres". Proceedings of the American Mathematical Society. 120 (4): 1223–1229. doi:10.1090/S0002-9939-1994-1172943-2. ISSN 0002-9939.
- ^ Bérard, P.; do Carmo, M.; Santos, W. (1998-06-01). "Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature". Annals of Global Analysis and Geometry. 16 (3): 273–290. doi:10.1023/A:1006542723958. ISSN 1572-9060. S2CID 189898400.
- ^ Barbosa, J. L. M.; Carmo, M. P. Do (2005-09-01). "On Stability of Cones in Rn+1 with Zero Scalar Curvature". Annals of Global Analysis and Geometry. 28 (2): 107–122. doi:10.1007/s10455-005-0039-5. ISSN 1572-9060. S2CID 122198627.
- ^ "zbMATH Open - the first resource for mathematics". zbmath.org. Retrieved 2022-02-01.
- ^ do Carmo, Manfredo P. (2012). Tenenblat, Keti (ed.). Manfredo P. do Carmo – Selected Papers. doi:10.1007/978-3-642-25588-5. ISBN 978-3-642-25587-8.
- ^ do Carmo, Manfredo P. (1994). "Differential Forms and Applications". Universitext. doi:10.1007/978-3-642-57951-6. ISBN 978-3-540-57618-1. ISSN 0172-5939.
- ^ Carmo, Manfredo Perdigão do (1992). Riemannian geometry. Francis J. Flaherty. Boston: Birkhäuser. ISBN 0-8176-3490-8. OCLC 24667701.
- ^ Shozo Motoyama, ed. (2004). Prelúdio para uma história: ciência e tecnologia no Brasil [Prelude for a story: science and technology in Brazil] (in Portuguese). EdUSP. p. 358. ISBN 978-85-314-0797-0.
- ^ Review by Mark Hunacek of Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo