Esfera tridimensional
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A esfera tridimensional ou hiperesfera é a mais simples variedade de dimensão 3.
Definição |
A esfera tridimensional é o conjunto
- S3={(x,y,z,t)∈R4:x2+y2+z2+t2=1}{displaystyle mathbb {S} ^{3}={(x,y,z,t)in mathbb {R} ^{4}:x^{2}+y^{2}+z^{2}+t^{2}=1}}
com a topologia induzida pela inclusão em R4{displaystyle mathbb {R} ^{4}}
.
Propriedades |
A esfera tridimensional:
- é compacta;
- tem grupo fundamental trivial;
- tem todos os grupos de homologia triviais excepto H0{displaystyle H_{0},}
e H3{displaystyle H_{3},}
que são Z{displaystyle mathbb {Z} }
.
Ver também |
Relatividade geral - várias soluções da Relatividade geral modelam o espaço como uma hiperesfera
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droooze
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