Weyl collineations that are not curvature collineations

Ibrar Hussain; Asghar Qadir; K. Saifullah

doi:10.1142/S021827180500695X

Weyl collineations that are not curvature collineations

Ibrar Hussain^*, Asghar Qadir, K. Saifullah

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel." Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality."

Original language	English
Pages (from-to)	1431-1437
Number of pages	7
Journal	International Journal of Modern Physics D
Volume	14
Issue number	8
DOIs	https://doi.org/10.1142/S021827180500695X
State	Published - Aug 2005

Bibliographical note

Funding Information:
Useful discussions with Ugur Camci are acknowledged. IH would like to thank the Higher Education Commission of Pakistan and Quaid-i-Azam University, Islamabad for financial support provided during this work.

Keywords

Curvature collineation
Lie algebra
Weyl collineations

ASJC Scopus subject areas

Mathematical Physics
Astronomy and Astrophysics
Space and Planetary Science

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10.1142/S021827180500695X

Cite this

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title = "Weyl collineations that are not curvature collineations",

abstract = "Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that {"}asymmetries cancel.{"} Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of {"}duality.{"}",

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author = "Ibrar Hussain and Asghar Qadir and K. Saifullah",

note = "Funding Information: Useful discussions with Ugur Camci are acknowledged. IH would like to thank the Higher Education Commission of Pakistan and Quaid-i-Azam University, Islamabad for financial support provided during this work.",

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doi = "10.1142/S021827180500695X",

language = "English",

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T1 - Weyl collineations that are not curvature collineations

AU - Hussain, Ibrar

AU - Qadir, Asghar

AU - Saifullah, K.

N1 - Funding Information: Useful discussions with Ugur Camci are acknowledged. IH would like to thank the Higher Education Commission of Pakistan and Quaid-i-Azam University, Islamabad for financial support provided during this work.

PY - 2005/8

Y1 - 2005/8

N2 - Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel." Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality."

AB - Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel." Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality."

KW - Curvature collineation

KW - Lie algebra

KW - Weyl collineations

UR - https://www.scopus.com/pages/publications/24144439307

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DO - 10.1142/S021827180500695X

M3 - Article

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SN - 0218-2718

VL - 14

SP - 1431

EP - 1437

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

IS - 8

ER -

Weyl collineations that are not curvature collineations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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