Generalized Einstein tensor for a Weyl manifold and its applications

dc.contributor.authorÖzdeğer, Abdülkadir
dc.date.accessioned2019-06-27T08:03:43Z
dc.date.available2019-06-27T08:03:43Z
dc.date.issued2013
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractIt is well known that the Einstein tensor G for a Riemannian manifold defined by R (alpha) (beta) = g (beta gamma) R (gamma I +/-) where R (gamma I +/-) and R are 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 theorems in Riemannian geometry. In this work we first obtain the generalized Einstein tensor for a Weyl manifold. Then after studying some properties of generalized Einstein tensor we prove that the conformal invariance of the generalized Einstein tensor implies the conformal invariance of the curvature tensor of the Weyl manifold and conversely. Moreover we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogonal trajectories of which are geodesics. Finally a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.en_US]
dc.identifier.citation2
dc.identifier.doi10.1007/s10114-012-0582-5en_US
dc.identifier.endpage382
dc.identifier.issn1439-8516en_US
dc.identifier.issn1439-7617en_US
dc.identifier.issn1439-8516
dc.identifier.issn1439-7617
dc.identifier.issue2
dc.identifier.scopus2-s2.0-84871972817en_US
dc.identifier.scopusqualityQ2
dc.identifier.startpage373en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12469/831
dc.identifier.urihttps://doi.org/10.1007/s10114-012-0582-5
dc.identifier.volume29en_US
dc.identifier.wosWOS:000313064700013en_US
dc.identifier.wosqualityQ3
dc.institutionauthorÖzdeğer, Abdülkadiren_US
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.journalActa Mathematica Sinica-English Seriesen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectWeyl manifolden_US
dc.subjectEinstein-Weyl manifolden_US
dc.subjectEinstein tensoren_US
dc.subjectGeneralized Einstein tensoren_US
dc.subjectGeneralized circleen_US
dc.titleGeneralized Einstein tensor for a Weyl manifold and its applicationsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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