Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

The outline of this research article is to initiate the development of a ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Y...

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Autores principales:	Pengfei Zhang, Yanlin Li, Soumendu Roy, Santu Dey
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Ricci–Yamabe soliton ∗-conformal <i>η</i>-Ricci–Yamabe soliton conformal killing vector field <i>α</i>-cosymplectic manifolds Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/cd28cb11b3b449c4a07c8dc49db8fc4e
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spelling	oai:doaj.org-article:cd28cb11b3b449c4a07c8dc49db8fc4e2021-11-25T19:07:27ZGeometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection10.3390/sym131121892073-8994https://doaj.org/article/cd28cb11b3b449c4a07c8dc49db8fc4e2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2189https://doaj.org/toc/2073-8994The outline of this research article is to initiate the development of a ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton equation when the potential vector field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cosymplectic metric as a ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.Pengfei ZhangYanlin LiSoumendu RoySantu DeyMDPI AGarticleRicci–Yamabe soliton∗-conformal <i>η</i>-Ricci–Yamabe solitonconformal killing vector field<i>α</i>-cosymplectic manifoldsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2189, p 2189 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Ricci–Yamabe soliton ∗-conformal <i>η</i>-Ricci–Yamabe soliton conformal killing vector field <i>α</i>-cosymplectic manifolds Mathematics QA1-939
spellingShingle	Ricci–Yamabe soliton ∗-conformal <i>η</i>-Ricci–Yamabe soliton conformal killing vector field <i>α</i>-cosymplectic manifolds Mathematics QA1-939 Pengfei Zhang Yanlin Li Soumendu Roy Santu Dey Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
description	The outline of this research article is to initiate the development of a ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton equation when the potential vector field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ξ</mi></semantics></math></inline-formula> of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-cosymplectic metric as a ∗-conformal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.
format	article
author	Pengfei Zhang Yanlin Li Soumendu Roy Santu Dey
author_facet	Pengfei Zhang Yanlin Li Soumendu Roy Santu Dey
author_sort	Pengfei Zhang
title	Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
title_short	Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
title_full	Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
title_fullStr	Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
title_full_unstemmed	Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection
title_sort	geometry of <i>α</i>-cosymplectic metric as ∗-conformal <i>η</i>-ricci–yamabe solitons admitting quarter-symmetric metric connection
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/cd28cb11b3b449c4a07c8dc49db8fc4e
work_keys_str_mv	AT pengfeizhang geometryofiaicosymplecticmetricasconformaliēiricciyamabesolitonsadmittingquartersymmetricmetricconnection AT yanlinli geometryofiaicosymplecticmetricasconformaliēiricciyamabesolitonsadmittingquartersymmetricmetricconnection AT soumenduroy geometryofiaicosymplecticmetricasconformaliēiricciyamabesolitonsadmittingquartersymmetricmetricconnection AT santudey geometryofiaicosymplecticmetricasconformaliēiricciyamabesolitonsadmittingquartersymmetricmetricconnection
_version_	1718410305618313216

Geometry of <i>α</i>-Cosymplectic Metric as ∗-Conformal <i>η</i>-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection

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