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On Einstein equations on manifolds and supermanifolds

Leites, D; Poletaeva, Elena LU and Serganova, V (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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Nonlinear Mathematical Physics
volume
9
issue
4
pages
394 - 425
publisher
Bokförlaget Atlantis
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
2007-11-14 13:12:15
date last changed
2017-01-01 06:46:29
@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    = {Bokförlaget Atlantis},
  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},
  volume       = {9},
  year         = {2002},
}