Manfredo Perdigão do Carmo (15 August 1928,

Maceió Maceió (), formerly anglicised as Maceio, is the capital and the largest city of the coastal state of Alagoas, Brazil. The name "Maceió" is an Indigenous term for a Spring (hydrology), spring. Most maceiós flow to the sea, but some get trapped ...

– 30 April 2018,

Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by population, second-most-populous city in Brazil (after São Paulo) and the Largest cities in the America ...

) was a Brazilian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He spent most of his career at IMPA and is seen as the doyen of

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

in Brazil.

Education and career

Do Carmo studied

civil engineering Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...

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. On suggestion of Elon Lima, in 1959 he went to

Instituto Nacional de Matemática Pura e Aplicada The ''Instituto Nacional de Matemática Pura e Aplicada'' (National Institute for Pure and Applied Mathematics) is considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is located in the cit ...

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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

under the supervision of

Shiing-Shen Chern Shiing-Shen Chern (; , ; October 26, 1911 – December 3, 2004) was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...

. 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

(IMPA) in

. From 2003 to his death he was

emeritus professor ''Emeritus/Emerita'' () is an honorary title granted to someone who retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". In some c ...

at the same institution. Do Carmo was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon and Olga Hirsh Guggenheim. These awards are bestowed upon individuals who have demonstrated d ...

1965 Events January–February * January 14 – The First Minister of Northern Ireland and the Taoiseach of the Republic of Ireland meet for the first time in 43 years. * January 20 ** Lyndon B. Johnson is Second inauguration of Lynd ...

and

1968 Events January–February * January 1968, January – The I'm Backing Britain, I'm Backing Britain campaign starts spontaneously. * January 5 – Prague Spring: Alexander Dubček is chosen as leader of the Communist Party of Cze ...

.Biography from the Guggenheim Foundation
/ref> In 1978 he was invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

held in

Helsinki Helsinki () is the Capital city, capital and most populous List of cities and towns in Finland, city in Finland. It is on the shore of the Gulf of Finland and is the seat of southern Finland's Uusimaa region. About people live in the municipali ...

. In 1991 he obtained a Doctorate ''

honoris causa An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hono ...

'' from Federal University of Alagoas and in 2012 from

University of Murcia The University of Murcia () is the primary institute of higher education in Murcia, Spain. With a student population of approximately 38,000, it is the largest university in the Region of Murcia. Founded in 1272 AD, the University of Murcia is ...

and from

Federal University of Amazonas The Federal University of Amazonas (, UFAM) is a public university A public university, state university, or public college is a university or college that is State ownership, owned by the state or receives significant funding from a governm ...

. He served as president of the Brazilian Mathematical Society in the term 1971–1973. He was elected a member of the

Brazilian Academy of Sciences Brazilian commonly refers to: * Brazil, a country * Brazilians, its people * Brazilian Portuguese, its dialect Brazilian may also refer to: * "The Brazilian", a 1986 instrumental music piece by Genesis * Brazilian Café, Baghdad, Iraq (1937) * Bra ...

in 1970, a member of

The World Academy of Sciences The World Academy of Sciences for the advancement of science in developing countries (TWAS) is a North–south research partnerships, merit-based science academy established for developing countries, uniting more than 1,400 scientists in some 1 ...

(TWAS) in 1997 and a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

In 2013. Among his awards, he received the Prêmio Almirante Álavaro Alberto from the

National Council for Scientific and Technological Development The National Council for Scientific and Technological Development (CNPq, , earlier ) is a government agency under the Ministry of Science and Technology of the Brazilian federal government. The council is dedicated to the promotion of scientific ...

in 1984, the TWAS Prize in Mathematics in 1992, the

National Order of Scientific Merit The National Order of Scientific Merit () is an honor bestowed upon Brazilian and foreign personalities recognized for their scientific and technical contributions to the cause and development of science in Brazil. It was instituted on March 16, 19 ...

in 1995 and the ''Comenda Graciliano Ramos'' from the municipality of

in 2000. Do Carmo died on 30 April 2018 at the age of 89.

Research

Do Carmo's main research interests were

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...

and the

differential geometry of surfaces In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth manifold, smooth Surface (topology), surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensiv ...

. In particular, he worked on rigidity and convexity of

isometric immersion In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is gi ...

s, stability of

hypersurface In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension , which is embedded in an ambient space of dimension , generally a Euclidea ...

s and of

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s, isoperimetric problems, minimal submanifolds of a

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

, and manifolds of constant

mean curvature In mathematics, the mean curvature H of a surface S is an ''extrinsic'' measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The ...

and vanishing

scalar curvature In the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry ...

. Do Carmo published more than 100 papers in peer-reviewed journals; in 2012 a selection of his works was published by

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

. He is also known for his textbooks: they were translated into many languages and used in courses from universities such as

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...

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

Books

*''Differential Geometry of Curves and Surfaces'',

Prentice-Hall Prentice Hall was a major American educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth century. In its last few years it ...

, 1976 .Review by Mark Hunacek of Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo
/ref> *''Riemannian Geometry'', Birkhäuser, 1992 *''Differential Forms and Applications'', Springer Verlag, Universitext, 1994 *(with Eduardo Wagner and Augusto Cezar de Oliveira Morgado). ''Trigonometria – Números Complexos''

References

{{DEFAULTSORT:Carmo, Manfredo do 1928 births 2018 deaths People from Maceió Differential geometers 20th-century Brazilian mathematicians University of California, Berkeley alumni Instituto Nacional de Matemática Pura e Aplicada researchers Fellows of the American Mathematical Society Members of the Brazilian Academy of Sciences Brazilian Mathematical Society TWAS laureates Textbook writers