Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 4
Pages
394 - 425
Publication Date
2002/11/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2002.9.4.3How to use a DOI?
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  -