An Unconventional Supergravity

  • Pavel Grozman
  • Dimitry Leites
Part of the NATO Science Series book series (NAII, volume 22)


We introduce and completely describe the analogues of the Riemann curvature tensor for the curved supergrassmannian of the passing through the origin (0|2)-dimensional subsupermanifolds in the (0|4)-dimensional supermanifold with the preserved volume form. The underlying manifold of this supergrassmannian is the conventional Penrose’s complexified and compactified version of the Minkowski space, i.e. the Grassmannian of 2-dimensional subspaces in the 4-dimensional space.

The result provides with yet another counterexample to Coleman-Mandula theorem.


Structure Function Minkowski Space Riemann Tensor Riemann Curvature Tensor Underlying Manifold 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Pavel Grozman
    • 1
  • Dimitry Leites
    • 1
  1. 1.Department of MathematicsUniversity of StockholmStockholmSweden

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