Volume 9, Issue 4, November 2002, Pages 394 - 425
On Einstein Equations on Manifolds and Supermanifolds
Authors
D. Leites, E. Poletaeva, V. Serganova
Corresponding Author
D. Leites
Received 27 February 2001, Revised 29 August 2001, Accepted 11 April 2002, Available Online 1 November 2002.
- DOI
- 10.2991/jnmp.2002.9.4.3How to use a DOI?
- Abstract
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].
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - D. Leites AU - E. Poletaeva AU - V. Serganova PY - 2002 DA - 2002/11/01 TI - On Einstein Equations on Manifolds and Supermanifolds JO - Journal of Nonlinear Mathematical Physics SP - 394 EP - 425 VL - 9 IS - 4 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.4.3 DO - 10.2991/jnmp.2002.9.4.3 ID - Leites2002 ER -