Volume 9, Issue 4, November 2001, Pages 394 - 425
On Einstein Equations on Manifolds and Supermanifolds
- D LEITES, E POLETAEVA, V SERGANOVA
- Corresponding Author
- D LEITES
Available Online 9 December 2006.
- https://doi.org/10.2991/jnmp.2002.9.4.3How to use a DOI?
- The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactifcation M becomes the Grassmannian Gr4 2 of 2-dimensional subspaces in the 4-dimesional complex one. Here we answer for which of the classical domains considered as manifolds with G-structure it is possible to impose conditions similar in some sense to EE. The above investigation has its counterpart on superdomains: an analog of the Riemann tensor is defined for any supermanifold with G-structure with any Lie supergroup G. We also derive similar analogues of EE on supermanifolds. Our analogs of EE are not what physicists consider as SUGRA (supergravity), for SUGRA see [16, 34].
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Cite this article
TY - JOUR AU - D LEITES AU - E POLETAEVA AU - V SERGANOVA PY - 2006 DA - 2006/12 TI - On Einstein Equations on Manifolds and Supermanifolds JO - Journal of Nonlinear Mathematical Physics SP - 394 EP - 425 VL - 9 IS - 4 SN - 1402-9251 UR - https://doi.org/10.2991/jnmp.2002.9.4.3 DO - https://doi.org/10.2991/jnmp.2002.9.4.3 ID - LEITES2006 ER -