A maximally symmetric space with torsion
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A maximally symmetric space, i.e., homogeneous and isotropic at every point, possessing totally antisymmetric torsion is dealt with. It is found that maximum symmetry restricts the dimension of the space to three. The three-curvature tensor for the space is obtained and from its form a three-metric is then constructed. The three-space is then allowed to evolve in time so that a four-metric of the formds2= −dt2+ (3)g ij dx i dx j is possible. From this an equation of motion is obtained which predicts an initial- and final-state singularity.
KeywordsDifferential Geometry Symmetric Space Maximum Symmetry Antisymmetric Torsion
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