Abstract
It is well known [1] that the three-dimensional space
of some models of closed homogeneous and isotropic universes has an especially simple geometry which can be seen best introducing a angular coordinate 0 ≤ ϰ ≤ π via r = R sin ϰ and transforming the line element (1) into the form
where
The metric (2) is that of a three-dimensional hypersurface of radius R which can be represented in a flat, four-dimensional Euclidean embedding space.
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Agnese, A.G., La Camera, M. (2001). Schwarzschild Metrics, Quasi-Universes and Wormholes. In: Sidharth, B.G., Altaisky, M.V. (eds) Frontiers of Fundamental Physics 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1339-1_18
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