Spheres and Euclidean Spaces Via Concircular Vector Fields

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dc.authoridDeshmukh, Sharief/0000-0003-3700-8164
dc.contributor.authorDeshmukh, Sharief
dc.contributor.authorIlarslan, Kazim
dc.contributor.authorAlsodais, Hana
dc.contributor.authorDe, Uday Chand
dc.date.accessioned2025-01-21T16:44:30Z
dc.date.available2025-01-21T16:44:30Z
dc.date.issued2021
dc.departmentKırıkkale Üniversitesi
dc.description.abstractIn this paper, we exhibit that non-trivial concircular vector fields play an important role in characterizing spheres, as well as Euclidean spaces. Given a non-trivial concircular vector field xi on a connected Riemannian manifold (M, g), two smooth functions s and. called potential function and connecting function are naturally associated to xi. We use non-trivial concircular vector fields on n-dimensional compact Riemannian manifolds to find four different characterizations of spheres S-n (c). In particular, we prove an interesting result namely an n-dimensional compact Riemannian manifold (M, g) that admits a non-trivial concircular vector field xi such that the Ricci operator is invariant under the flow of xi, if and only if, (M, g) is isometric to a sphere Sn (c). Similarly, we find two characterizations of Euclidean spaces E-n. In particular, we show that an n-dimensional complete and connected Riemannian manifold (M, g) admits a non-trivial concircular vector field xi that annihilates the Ricci operator, if and only if, (M, g) is isometric to the Euclidean space E-n.
dc.description.sponsorshipDeanship of Scientific Research, King Saud University [RG-1441-P182]
dc.description.sponsorshipThe authors extend their appreciations to the Deanship of Scientific Research, King Saud University for funding this work through research Group No (RG-1441-P182).
dc.identifier.doi10.1007/s00009-021-01869-4
dc.identifier.issn1660-5446
dc.identifier.issn1660-5454
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85114425295
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s00009-021-01869-4
dc.identifier.urihttps://hdl.handle.net/20.500.12587/25476
dc.identifier.volume18
dc.identifier.wosWOS:000695493100010
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer Basel Ag
dc.relation.ispartofMediterranean Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241229
dc.subjectConcircular vector field; Isometric to sphere; Isometric to Euclidean space
dc.titleSpheres and Euclidean Spaces Via Concircular Vector Fields
dc.typeArticle

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