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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.
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.
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} .
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 ...
The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection that is torsion-free and metric-compatible, called the Levi-Civita connection or (pseudo-) Riemannian connection of the given metric.
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.
Foxit PhantomPDF, a multi-feature PDF editor, was released in 2008. Foxit PhantomPDF has an interface that holds many advanced PDF editing and security features. [30] Foxit released version 8.0 in 2016. [25] The software has been renamed from Foxit PhantomPDF to Foxit PDF Editor with the release of Foxit PDF Editor 11.0.0.49893 dated May 25 ...
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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