A 4-sphere has positive curvature, with
(1)
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(2)
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Since
(3)
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(4)
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(5)
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To stay on the surface of the sphere,
(6)
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(7)
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(8)
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(9)
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(10)
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(11)
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With the addition of the so-called expansion parameter, this is the Robertson-Walker line element.