embedded manifold

[/ɛmˈbɛdɪd ˈmænɪfoʊld/]
nounpl: embedded manifolds
variedade embutida
1. In mathematics and differential geometry, a smooth manifold that is placed or situated within another manifold (typically Euclidean space) via a smooth injective immersion that is also a topological embedding
The sphere is a classic example of an embedded manifold in three-dimensional Euclidean space.
A esfera é um exemplo clássico de variedade embutida no espaço euclidiano tridimensional.
2. A submanifold that preserves the differential structure of the larger ambient space it is embedded in
When studying embedded manifolds, mathematicians examine how intrinsic properties relate to extrinsic geometric properties.
Ao estudar variedades embutidas, matemáticos examinam como propriedades intrínsecas se relacionam com propriedades geométricas extrínsecas.
This is specialized mathematical terminology used primarily in academic and research contexts. The term 'variedade embutida' is standard in Brazilian mathematical literature, while Portugal may use 'variedade mergulhada' (literally 'immersed variety'). The concept is fundamental in differential geometry courses taught in both Brazil and Portugal at the university level.
Synonyms / Sinônimos
submanifoldimmersed manifoldembedded submanifold
Antonyms / Antônimos
abstract manifoldimmersed manifold (when not embedded)

Regional Variations

General Brazilian
variedade embutida
Standard mathematical terminology used in Brazilian universities
Portugal
variedade mergulhada
Alternative Portuguese terminology, more common in European Portuguese mathematical texts
São Paulo
variedade embutida
Preferred term in São Paulo's major mathematics departments

Related Words

manifolddifferential geometryimmersionsubmanifoldEuclidean spacesmooth mappingtopological embedding
Look up more words on Fala2Me
The free English-Portuguese dictionary with real Brazilian accents, NYC slang, conjugator and more
Open Fala2Me →