Brazilian mathematician
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
[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
References
^ 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 [
pt ] . 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
International National Academics Other