Journal of Nonlinear Mathematical Physics

Volume 9, Issue 4, November 2001, Pages 394 - 425

On Einstein Equations on Manifolds and Supermanifolds

Authors
D LEITES, E POLETAEVA, V SERGANOVA
Corresponding Author
D LEITES
Available Online 9 December 2006.
DOI
https://doi.org/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].
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 4
Pages
394 - 425
Publication Date
2006/12
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.4.3How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

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  -