Generalized Einstein’s tensor for a Weyl manifold and its applications

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dc.contributor.authorÖzdeğer, Abdülkadir
dc.date.accessioned2024-07-12T20:51:17Z
dc.date.available2024-07-12T20:51:17Z
dc.date.issued2009en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractA differentiable manifold having a torsion-free connection ? and a conformal class C[g] of metrics which is preserved by ? is called a Weyl manifold. The condition involved in this definition can be expressed as ?g = 2(g ? w) for some 1-form w [1] . It is well known that Einstein’s tensor G for a Riemannian manifold defined by G? ? = R ? ? ? 1 2 ? ? ?R, R? ? = g ??R?? where R ? ? and R respectively the Ricci tensor and the scalar curvature of the manifold , plays an important part in Einstein’s theory of gravitation as well as in proving some basic theorems in Riemannian geometry [2]. In this work , we obtain the generalized Einstein’s tensor for Weyl manifolds by using the second Bianchi identity for such manifolds obtained in [3] . Then, we deduce the following results : (a) Any 2-dimensional Einstein-Weyl manifold has a vanishing generalized Einstein’s tensor, (b) A Weyl manifold and its Liouville transformation have the same generalized Einstein’s tensor, (c) If the 1-form w for an Einstein-Weyl manifold is locally a gradient, then the scalar curvature of the manifold is prolonged covariant constant.en_US
dc.identifier.citationÖzdeğer, A. (2009). Generalized Einstein’s tensor for a Weyl manifold and its applications. Maltepe Üniversitesi. s. 64.en_US
dc.identifier.endpage65en_US
dc.identifier.isbn9.78605E+12
dc.identifier.startpage64en_US
dc.identifier.urihttps://www.maltepe.edu.tr/Content/Media/CkEditor/03012019014112056-AbstractBookICMS2009Istanbul.pdf#page=76
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2393
dc.institutionauthorÖzdeğer, Abdülkadir
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY07758
dc.titleGeneralized Einstein’s tensor for a Weyl manifold and its applicationsen_US
dc.typeConference Object
dspace.entity.typePublication

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