Trans-Sasakian static spaces

Static spaces (with perfect fluids) appeared in a natural way both in physics (cf. Hawking and Ellis, 1975) and mathematics (cf. A. Fischer and J. Marsden, Duke Math. J. 42 (3) (1975), 519–547). These arise as solutions of the perfect static fluid equation and play a key role in general relativity,...

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Autores principales:	Ibrahim Al-Dayel, Sharief Deshmukh, Gabriel-Eduard Vîlcu
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Trans-Sasakian manifold Sasakian manifold Einstein Sasakian manifold Scalar curvature Static perfect fluid equation Physics QC1-999
Acceso en línea:	https://doaj.org/article/bc1f5809466c4d459acc99e63e868573
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id	oai:doaj.org-article:bc1f5809466c4d459acc99e63e868573
record_format	dspace
spelling	oai:doaj.org-article:bc1f5809466c4d459acc99e63e8685732021-12-04T04:33:51ZTrans-Sasakian static spaces2211-379710.1016/j.rinp.2021.105009https://doaj.org/article/bc1f5809466c4d459acc99e63e8685732021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2211379721010093https://doaj.org/toc/2211-3797Static spaces (with perfect fluids) appeared in a natural way both in physics (cf. Hawking and Ellis, 1975) and mathematics (cf. A. Fischer and J. Marsden, Duke Math. J. 42 (3) (1975), 519–547). These arise as solutions of the perfect static fluid equation and play a key role in general relativity, providing patterns for some celestial objects. In this paper, we investigate compact and simply connected trans-Sasakian spaces having type (α,β), whose defining functions α and β satisfy the static perfect fluid equation. In particular, we derive some conditions that ensure these spaces are isometric to a 3-sphere. First result of this work shows that the function α satisfying static perfect fluid equation and the scalar curvature τ satisfying certain inequality are not only necessary, but also sufficient conditions for a 3-dimensional compact and simply connected trans-Sasakian manifold to be isometric to a 3-sphere. In the second result of this paper, we prove that the function β satisfying the static perfect fluid equation, scalar curvature τ satisfying certain inequality and the Ricci operator satisfying a Coddazi-type equation are also requirements ensuring that a trans-Sasakian space (again compact and also simply connected) is isometric with a 3-sphere.Ibrahim Al-DayelSharief DeshmukhGabriel-Eduard VîlcuElsevierarticleTrans-Sasakian manifoldSasakian manifoldEinstein Sasakian manifoldScalar curvatureStatic perfect fluid equationPhysicsQC1-999ENResults in Physics, Vol 31, Iss , Pp 105009- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Trans-Sasakian manifold Sasakian manifold Einstein Sasakian manifold Scalar curvature Static perfect fluid equation Physics QC1-999
spellingShingle	Trans-Sasakian manifold Sasakian manifold Einstein Sasakian manifold Scalar curvature Static perfect fluid equation Physics QC1-999 Ibrahim Al-Dayel Sharief Deshmukh Gabriel-Eduard Vîlcu Trans-Sasakian static spaces
description	Static spaces (with perfect fluids) appeared in a natural way both in physics (cf. Hawking and Ellis, 1975) and mathematics (cf. A. Fischer and J. Marsden, Duke Math. J. 42 (3) (1975), 519–547). These arise as solutions of the perfect static fluid equation and play a key role in general relativity, providing patterns for some celestial objects. In this paper, we investigate compact and simply connected trans-Sasakian spaces having type (α,β), whose defining functions α and β satisfy the static perfect fluid equation. In particular, we derive some conditions that ensure these spaces are isometric to a 3-sphere. First result of this work shows that the function α satisfying static perfect fluid equation and the scalar curvature τ satisfying certain inequality are not only necessary, but also sufficient conditions for a 3-dimensional compact and simply connected trans-Sasakian manifold to be isometric to a 3-sphere. In the second result of this paper, we prove that the function β satisfying the static perfect fluid equation, scalar curvature τ satisfying certain inequality and the Ricci operator satisfying a Coddazi-type equation are also requirements ensuring that a trans-Sasakian space (again compact and also simply connected) is isometric with a 3-sphere.
format	article
author	Ibrahim Al-Dayel Sharief Deshmukh Gabriel-Eduard Vîlcu
author_facet	Ibrahim Al-Dayel Sharief Deshmukh Gabriel-Eduard Vîlcu
author_sort	Ibrahim Al-Dayel
title	Trans-Sasakian static spaces
title_short	Trans-Sasakian static spaces
title_full	Trans-Sasakian static spaces
title_fullStr	Trans-Sasakian static spaces
title_full_unstemmed	Trans-Sasakian static spaces
title_sort	trans-sasakian static spaces
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/bc1f5809466c4d459acc99e63e868573
work_keys_str_mv	AT ibrahimaldayel transsasakianstaticspaces AT shariefdeshmukh transsasakianstaticspaces AT gabrieleduardvilcu transsasakianstaticspaces
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Trans-Sasakian static spaces

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