differentiable manifolds
[ˌdɪfərˈɛnʃəbəl məˈnɪfoʊldz]
nounpl: differentiable manifolds
variedades diferenciáveis
1. A topological space that locally resembles Euclidean space and has a smooth structure allowing differentiation of functions defined on it
Differentiable manifolds are fundamental objects in differential geometry and theoretical physics.
Variedades diferenciáveis são objetos fundamentais em geometria diferencial e física teórica.
2. A mathematical space equipped with charts that allow for the application of calculus in a consistent manner
The sphere is an example of a differentiable manifold that is compact and without boundary.
A esfera é um exemplo de variedade diferenciável que é compacta e sem fronteira.
3. A generalization of curves and surfaces to higher dimensions with a well-defined notion of smoothness
General relativity describes spacetime as a 4-dimensional differentiable manifold.
A relatividade geral descreve o espaço-tempo como uma variedade diferenciável de 4 dimensões.
This is technical terminology primarily used in academic and research settings in mathematics, physics, and engineering. Both Brazil and Portugal use the term 'variedades diferenciáveis' in their respective mathematical communities. The concept is central to modern differential geometry and is taught in advanced undergraduate and graduate mathematics courses in both countries.
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