On Einstein equations on manifolds and supermanifolds
(2002) In Journal of Nonlinear Mathematical Physics 9(4). p.394-425- 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 compactification M becomes the Grassmannian Gr(2)(4) of 2-dimensional subspaces in the 4-dimensional 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 super manifold 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... (More)
- The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactification M becomes the Grassmannian Gr(2)(4) of 2-dimensional subspaces in the 4-dimensional 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 super manifold 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]. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/324205
- author
- Leites, D ; Poletaeva, Elena LU and Serganova, V
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Nonlinear Mathematical Physics
- volume
- 9
- issue
- 4
- pages
- 394 - 425
- publisher
- Taylor & Francis
- external identifiers
-
- wos:000179029400003
- scopus:0036433811
- ISSN
- 1402-9251
- DOI
- 10.2991/jnmp.2002.9.4.3
- language
- English
- LU publication?
- yes
- id
- 76150bd8-dfec-4508-80b8-64baff27503f (old id 324205)
- date added to LUP
- 2016-04-01 15:46:54
- date last changed
- 2022-01-28 07:00:31
@article{76150bd8-dfec-4508-80b8-64baff27503f,
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 compactification M becomes the Grassmannian Gr(2)(4) of 2-dimensional subspaces in the 4-dimensional 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 super manifold 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].}},
author = {{Leites, D and Poletaeva, Elena and Serganova, V}},
issn = {{1402-9251}},
language = {{eng}},
number = {{4}},
pages = {{394--425}},
publisher = {{Taylor & Francis}},
series = {{Journal of Nonlinear Mathematical Physics}},
title = {{On Einstein equations on manifolds and supermanifolds}},
url = {{http://dx.doi.org/10.2991/jnmp.2002.9.4.3}},
doi = {{10.2991/jnmp.2002.9.4.3}},
volume = {{9}},
year = {{2002}},
}