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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.
do Carmo, Manfredo P. (2016). Differential geometry of curves & surfaces (Revised & updated second edition of 1976 original ed.). Mineola, NY: Dover Publications, Inc. ISBN 978-0-486-80699-0. MR 3837152. Zbl 1352.53002. Kobayashi, Shoshichi; Nomizu, Katsumi (1969). Foundations of differential geometry. Volume II. Interscience Tracts in Pure and ...
This proof is basically the same as in Hilbert's paper, although based in the books of Do Carmo and Spivak. Observations : In order to have a more manageable treatment, but without loss of generality , the curvature may be considered equal to minus one, K = − 1 {\displaystyle K=-1} .
In 1841 Delaunay proved that the only surfaces of revolution with constant mean curvature were the surfaces obtained by rotating the roulettes of the conics. These are the plane, cylinder, sphere, the catenoid, the unduloid and nodoid.
In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas [1]) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.
Do Carmo is a surname. Notable people with the surname include: Allan do Carmo (born 1989), Brazilian swimmer; Carlos do Carmo (1939–2021), Portuguese fado singer; Chiquito do Carmo (born 1986), East Timorese footballer
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