Abstract
A geometric formulation of the gravitation theory in the spacetime R × S3 is given. A linear connection is introduced on the tangent bundle T(R × S3) and then the connection coefficients and the Riemann curvature tensor are calculated. It is shown that their expressions differ from those of Carmeli and Malin [Found. Phys.17, 407 (1987)] by supplementary terms due to the noncommutativity of derivatives used on the spacetime R × S3. The Einstein field equations are written as usually and a comparison with other results is given. Finally, some observations about a possible gauge theory of gravitation in the spacetime R × S3 are made.
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Zet, G., Pasnicu, C. & Agop, M. Gravitation theory in the spacetimeR×S 3 . Found Phys 21, 473–481 (1991). https://doi.org/10.1007/BF00733359
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DOI: https://doi.org/10.1007/BF00733359