General Relativity and Gravitation

, Volume 9, Issue 9, pp 763–771 | Cite as

A maximally symmetric space with torsion

  • Iris Bloomer
Research Articles


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.


Differential Geometry Symmetric Space Maximum Symmetry Antisymmetric Torsion 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Iris Bloomer
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley

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