Wikipedia

Manfredo do Carmo

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
do Carmo in 1979
Born(1928-08-15)15 August 1928
Maceió, Alagoas
Died30 April 2018(2018-04-30) (aged 89)
Rio de Janeiro
Resting placeCemitério de São João Batista
NationalityBrazilian
Alma materUniversity of California, Berkeley
AwardsGuggenheim Fellowship (1965, 1968)
Prêmio Almirante Álavaro Alberto (1984)
Brazil's National Order of Scientific Merit (1995)
TWAS Prize (1987)
AMS Fellow (2012)
Scientific career
FieldsMathematics
InstitutionsInstituto Nacional de Matemática Pura e Aplicada
Thesis The Cohomology Ring of Certain Kahlerian Manifolds  (1963)
Doctoral advisorShiing-Shen Chern
Doctoral studentsCelso Costa
Marcos Dajczer
Keti Tenenblat

Education and career

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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

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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

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  • 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

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  1. ^ 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.
  2. ^ 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.
  3. ^ 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
  4. ^ a b Manfredo do Carmo at the Mathematics Genealogy Project
  5. ^ Biography from the Guggenheim Foundation
  6. ^ "John Simon Guggenheim Foundation | Manfredo Perdigao do Carmo". Retrieved 2022-01-31.
  7. ^ Lehto, Olii, ed. (1980). Proceedings of the International Congress of Mathematician 1978 (PDF). Helsinki. p. 401.{{cite book}}: CS1 maint: location missing publisher (link)
  8. ^ 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.
  9. ^ 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
  10. ^ "Ufal promove evento internacional na área de Matemática" [Ufal promotes international event in an area of mathematics]. Universidade Federal de Alagoas (in Brazilian Portuguese). 12 March 2014. Retrieved 2022-02-07.
  11. ^ "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). 8 June 2018. Retrieved 2022-02-07.
  12. ^ "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.
  13. ^ Laudatio del Padrino (in Spanish), 2012-05-15, retrieved 2022-02-06
  14. ^ "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).
  15. ^ "Resolução N° 009/2012" (PDF) (in Portuguese).
  16. ^ "Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática" (in Brazilian Portuguese). Retrieved 2022-01-31.
  17. ^ "Manfredo Perdigão do Carmo – ABC" (in Brazilian Portuguese). Retrieved 2022-01-31.
  18. ^ a b "do Carmo, Manfredo P." TWAS. Retrieved 2022-01-31.
  19. ^ List of Fellows of the American Mathematical Society, retrieved 2015-01-13.
  20. ^ "CNPq - Prêmio Almirante Álvaro Alberto". www.premioalvaroalberto.cnpq.br (in Portuguese). Retrieved 2022-02-01.
  21. ^ "Prizes and Awards". The World Academy of Sciences. 2016.
  22. ^ "Ordem Nacional do Mérito Científico" (in Portuguese). Instituto Brasileiro de Informação em Ciência e Tecnologia [pt]. 11 August 2023.
  23. ^ "Matemático Manfredo do Carmo morre aos 89 anos" [Mathematician Manfredo do Carmo dies at age 89] (in Portuguese). IMPA. Retrieved 1 May 2018.
  24. ^ "Decease of Prof. Do Carmo | European Mathematical Society". euro-math-soc.eu. Retrieved 2022-01-31.
  25. ^ "News from the AMS". American Mathematical Society. Retrieved 2022-01-31.
  26. ^ 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.
  27. ^ 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.
  28. ^ 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.
  29. ^ 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.
  30. ^ 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.
  31. ^ 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.
  32. ^ 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.
  33. ^ 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.
  34. ^ 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
  35. ^ 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.
  36. ^ 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.
  37. ^ 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.
  38. ^ 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.
  39. ^ 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.
  40. ^ 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.
  41. ^ "zbMATH Open - the first resource for mathematics". zbmath.org. Retrieved 2022-02-01.
  42. ^ 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.
  43. ^ 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.
  44. ^ Carmo, Manfredo Perdigão do (1992). Riemannian geometry. Francis J. Flaherty. Boston: Birkhäuser. ISBN 0-8176-3490-8. OCLC 24667701.
  45. ^ 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.
  46. ^ Review by Mark Hunacek of Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo
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