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Ricci flow for homogeneous compact models of the universe. (English) Zbl 1230.83030

Summary: Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
11R32 Galois theory
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53Z05 Applications of differential geometry to physics
83-03 History of relativity and gravitational theory
01A60 History of mathematics in the 20th century
83-08 Computational methods for problems pertaining to relativity and gravitational theory
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