Manfredo do Carmo explained

Manfredo do Carmo
Birth Date:15 August 1928
Birth Place:Maceió, Alagoas
Death Place:Rio de Janeiro
Resting Place:Cemitério de São João Batista
Nationality:Brazilian
Fields:Mathematics
Workplaces:Instituto Nacional de Matemática Pura e Aplicada
Alma Mater:University of California, Berkeley
Thesis Title:The Cohomology Ring of Certain Kahlerian Manifolds
Thesis Year:1963
Doctoral Advisor:Shiing-Shen Chern
Doctoral Students:Celso Costa
Marcos Dajczer
Keti Tenenblat
Awards:Guggenheim Fellowship (1965, 1968)
Prêmio Almirante Álavaro Alberto (1984)
Brazil's National Order of Scientific Merit (1995)
TWAS Prize (1987)
AMS Fellow (2012)

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]

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 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.

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.

Do Carmo was a Guggenheim Fellow in 1965 and 1968.[3] [4] In 1978 he was invited speaker at the International Congress of Mathematicians held in Helsinki.[5] [6] In 1991 he obtained a Doctorate honoris causa from Federal University of Alagoas[7] [8] and in 2012 from University of Murcia[9] and from Federal University of Amazonas.[10] [11]

He served as president of the Brazilian Mathematical Society in the term 1971–1973.[12] He was elected a member of the Brazilian Academy of Sciences in 1970,[13] a member of The World Academy of Sciences (TWAS) in 1997[14] and a fellow of the American Mathematical Society In 2013.[15]

Among his awards, he received the Prêmio Almirante Álavaro Alberto from the National Council for Scientific and Technological Development in 1984,[16] the TWAS Prize in Mathematics in 1992,[14] [17] the National Order of Scientific Merit in 1995[18] and the Comenda Graciliano Ramos from the municipality of Maceió in 2000.

Do Carmo died on 30 April 2018 at the age of 89.[19] [20] [21]

Research

Do Carmo's main research interests were Riemannian geometry and the differential geometry of surfaces.

In particular, he worked on rigidity and convexity of isometric immersions,[22] [23] stability of hypersurfaces[24] [25] and of minimal surfaces,[26] [27] topology of manifolds,[28] isoperimetric problems,[29] minimal submanifolds of a sphere,[30] and manifolds of constant mean curvature[31] [32] [33] [34] and vanishing scalar curvature.[35]

Do Carmo published more than 100 papers in peer-reviewed journals;[36] in 2012 a selection of his works was published by Springer.[37] He is also known for his textbooks:[38] [39] they were translated into many languages and used in courses from universities such as Harvard and Columbia.[40]

He supervised 27 PhD students, including Celso Costa, Marcos Dajczer and Keti Tenenblat.

Books

Notes and References

  1. Gorodski. Claudio. Piccione. Paolo. 2021-06-01. Opening note: An homage to Manfredo P. do Carmo. São Paulo Journal of Mathematical Sciences. en. 15. 1. 1–2. 10.1007/s40863-020-00194-0. 228984989. 2316-9028. free.
  2. 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. pt. 7. 20. 266–276. 10.30938/bocehm.v7i20.2819. 225625329. 2447-8504. free.
  3. https://web.archive.org/web/20150113232909/http://www.gf.org/fellows/2288-manfredo-perdigao-do-carmo Biography from the Guggenheim Foundation
  4. Web site: John Simon Guggenheim Foundation Manfredo Perdigao do Carmo. 2022-01-31. en-US.
  5. Book: Proceedings of the International Congress of Mathematician 1978. 1980. Lehto. Olii. Olli Lehto. Helsinki. 401.
  6. .
  7. Web site: Ufal promove evento internacional na área de Matemática. Ufal promotes international event in an area of mathematics. 2022-02-07. Universidade Federal de Alagoas. pt-br.
  8. Web site: Alagoano referência em geometria diferencial será homenageado em evento. Alagoan reference in differential geometry will be homaged in an event. 2022-02-07. Universidade Federal de Alagoas. pt-br.
  9. Web site: Professor Manfredo P. Do Carmo will be awarded the honorary degree Doctor Honoris Causa by the Universidad de Murcia European Mathematical Society. 2022-02-01. euro-math-soc.eu.
  10. Web site: Ata da sessão solene de outorga de titulo Dr. Honoris Causa. Acts of the solemn session to grant the title of Dr. Honoris Causa. pt.
  11. Web site: Resolução N° 009/2012. pt.
  12. Web site: Diretorias Anteriores – SBM – Sociedade Brasileira de Matemática. 2022-01-31. pt-BR.
  13. Web site: Manfredo Perdigão do Carmo – ABC. 2022-01-31. pt-BR.
  14. Web site: do Carmo, Manfredo P.. 2022-01-31. TWAS. en.
  15. https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society
  16. Web site: CNPq - Prêmio Almirante Álvaro Alberto. 2022-02-01. www.premioalvaroalberto.cnpq.br. pt.
  17. Web site: 2016. Prizes and Awards. The World Academy of Sciences.
  18. Web site: Ordem Nacional do Mérito Científico. 11 August 2023 . . pt.
  19. Web site: Matemático Manfredo do Carmo morre aos 89 anos. Mathematician Manfredo do Carmo dies at age 89. 1 May 2018. IMPA. pt.
  20. Web site: Decease of Prof. Do Carmo European Mathematical Society. 2022-01-31. euro-math-soc.eu.
  21. Web site: News from the AMS. 2022-01-31. American Mathematical Society. en.
  22. do Carmo. M. P.. Warner. F. W.. 1970. Rigidity and convexity of hypersurfaces in spheres. Journal of Differential Geometry. 4. 2. 10.4310/jdg/1214429378. 0022-040X. free.
  23. doCarmo. Manfredo P.. Lima. Elon. 1969-05-01. Isometric immersions with semi-definite second quadratic forms. Archiv der Mathematik. en. 20. 2. 173–175. 10.1007/BF01899010. 189777457. 1420-8938.
  24. Barbosa. João Lucas. do Carmo. Manfredo. 1984-09-01. Stability of hypersurfaces with constant mean curvature. Mathematische Zeitschrift. en. 185. 3. 339–353. 10.1007/BF01215045. 186222313. 1432-1823.
  25. Barbosa. J. Lucas. do Carmo. Manfredo. Eschenburg. Jost. 1988-03-01. Stability of hypersurfaces of constant mean curvature in Riemannian manifolds. Mathematische Zeitschrift. en. 197. 1. 123–138. 10.1007/BF01161634. 186231004. 1432-1823.
  26. 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. 10.2307/2373899. 2373899. 0002-9327.
  27. do Carmo. M.. Peng. C. K.. 1979. Stable complete minimal surfaces in ³ are planes. Bulletin of the American Mathematical Society. en. 1. 6. 903–906. 10.1090/S0273-0979-1979-14689-5. 0273-0979. free.
  28. do Carmo. Manfredo. Xia. Changyu. 2000-02-01. Ricci curvature and the topology of open manifolds. Mathematische Annalen. en. 316. 2. 391–400. 10.1007/s002080050018. 189881132. 1432-1807.
  29. Barbosa. João Lucas. Carmo. Manfredo do. 1978-10-01. A proof of a general isoperimetric inequality for surfaces. Mathematische Zeitschrift. en. 162. 3. 245–261. 10.1007/BF01186367. 186236970. 1432-1823.
  30. Carmo. Manfredo P. Do. Wallach. Nolan R.. 1971. Minimal Immersions of Spheres into Spheres. Annals of Mathematics. 93. 1. 43–62. 10.2307/1970752. 1970752. 0003-486X.
  31. do Carmo. Manfredo P.. Dajczer. Marcos. 1982-01-01. Helicoidal surfaces with constant mean curvature. Tohoku Mathematical Journal. 34. 3. 10.2748/tmj/1178229204. 109931575 . 0040-8735. free.
  32. Carmo. M. Do. Dajczer. M.. 1983. Rotation Hypersurfaces in Spaces of Constant Curvature. Transactions of the American Mathematical Society. 277. 2. 685–709. 10.2307/1999231. 1999231. 0002-9947.
  33. Alencar. Hilário. do Carmo. Manfredo. 1994. Hypersurfaces with constant mean curvature in spheres. Proceedings of the American Mathematical Society. en. 120. 4. 1223–1229. 10.1090/S0002-9939-1994-1172943-2. 0002-9939. free.
  34. 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. en. 16. 3. 273–290. 10.1023/A:1006542723958. 189898400. 1572-9060.
  35. 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. en. 28. 2. 107–122. 10.1007/s10455-005-0039-5. 122198627. 1572-9060.
  36. Web site: zbMATH Open - the first resource for mathematics. 2022-02-01. zbmath.org.
  37. Book: do Carmo, Manfredo P.. Keti. Tenenblat. 2012. Manfredo P. do Carmo – Selected Papers. en-gb. 10.1007/978-3-642-25588-5. 978-3-642-25587-8.
  38. do Carmo. Manfredo P.. 1994. Differential Forms and Applications. Universitext. en-gb. 10.1007/978-3-642-57951-6. 978-3-540-57618-1. 0172-5939.
  39. Book: Carmo, Manfredo Perdigão do. Riemannian geometry. 1992. Birkhäuser. Francis J. Flaherty. 0-8176-3490-8. Boston. 24667701.
  40. Book: Prelúdio para uma história: ciência e tecnologia no Brasil. EdUSP. 2004. 978-85-314-0797-0. Shozo Motoyama. 358. pt. Prelude for a story: science and technology in Brazil.
  41. https://maa.org/press/maa-reviews/differential-geometry-of-curves-and-surfaces-1 Review by Mark Hunacek of Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo

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