Product submanifolds with pointwise 3-planar normal sections

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dc.contributor.authorWest, Alan
dc.contributor.buuauthorArslan, Kadri
dc.contributor.departmentUludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.tr_TR
dc.contributor.orcid0000-0002-1440-7050tr_TR
dc.contributor.researcheridAAG-8775-2021tr_TR
dc.date.accessioned2021-07-05T05:16:49Z
dc.date.available2021-07-05T05:16:49Z
dc.date.issued1995
dc.description.abstractLet M be a smooth m-dimensional submanifold in (m + d)- dimensional Euclidean space Um+d. For x e M and a non-zero vector X in TXM, we define the (d + l)-dimensional affine subspace E(x,X) of Um+d by E(x, X) = x + spw{X, NX(M)}. In a neighbourhood of x, the intersection M DE(x,X) is a regular curve y:(-e , e)—»M. We suppose the parameter f e (-e, e) is a multiple of the arc-length such that y(0) = x and y(0) = X. Each choice of X e T(M) yields a different curve which is called the normal section of M at JC in the direction of X, where X s TX(M) (Section 3). For such a normal section we can write y(t) = x + \(t)X + N(t). (0.1) where N(t) e NX(M) and A(f) e R. The submanifold M is said to have pointwise k-planar normal sections (Pk-PNS) if for each normal section y the first, second and higher order derivatives are linearly dependent as vectors in Mn+d. Submanifolds with pointwise 3-planar normal sections have been studied by S. J. Li in the case when M is isotropic [6] and also in the case when M is spherical [7]. In this paper we consider product submanifolds M = MXX M2 with P3-PNS and we show that this implies strong conditions on Mj and M2en_US
dc.identifier.citationArslan, K. ve West, A. (1995). ''Product submanifolds with pointwise 3-planar normal sections''. Glasgow Mathematical Journal, 37(1), 73-81.en_US
dc.identifier.endpage81tr_TR
dc.identifier.issn0017-0895
dc.identifier.issue1tr_TR
dc.identifier.scopus2-s2.0-2442479202tr_TR
dc.identifier.startpage73tr_TR
dc.identifier.urihttps://doi.org/10.1017/S001708950003041X
dc.identifier.urihttps://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/product-submanifolds-with-pointwise-3planar-normal-sections/5B70E551708FC84BC9DA7B659FABD57C
dc.identifier.urihttp://hdl.handle.net/11452/21015
dc.identifier.volume37tr_TR
dc.identifier.wosA1995QL38900010tr_TR
dc.indexed.scopusScopusen_US
dc.indexed.wosSCIEen_US
dc.language.isoenen_US
dc.publisherOxford Univ Press United Kingdomen_US
dc.relation.collaborationYurt dışıtr_TR
dc.relation.journalGlasgow Mathematical Journaltr_TR
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergitr_TR
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMathematicsen_US
dc.subject.wosMathematicsen_US
dc.titleProduct submanifolds with pointwise 3-planar normal sectionsen_US
dc.typeArticle

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