A Note on Surfaces in Space Forms with Pythagorean Fundamental Forms

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dc.contributor.authorAydin, Muhittin Evren
dc.contributor.authorMihai, Adela
dc.date.accessioned2026-08-12T17:50:16Z
dc.date.issued2020
dc.departmentFırat Üniversitesi
dc.description.abstractIn the present note we introduce a Pythagorean-like formula for surfaces immersed into 3-dimensional space forms mml:semantics M3(c)mml:semantics of constant sectional curvature mml:semantics c=-1,0,1.mml:semantics> More precisely, we consider a surface immersed into c mml:mfenced /mml:semantics satisfying mml:semantics 2+II2=III2,mml:semantics where mml:semanticsImml:semantics, mml:semanticsIImml:semantics and mml:semantics>IIImml:semantics> are the matrices corresponding to the first, second and third fundamental forms of the surface, respectively. We prove that such a surface is a totally umbilical round sphere with Gauss curvature mml:semantics phi +c,mml:semantics where mml:semantics phi mml:semantics is the Golden ratio.
dc.identifier.doi10.3390/math8030444
dc.identifier.issn2227-7390
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85082428673
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.3390/math8030444
dc.identifier.urihttps://hdl.handle.net/11508/62147
dc.identifier.volume8
dc.identifier.wosWOS:000524085900143
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofMathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260511
dc.subjectPythagorean formula
dc.subjectGolden ratio
dc.subjectGauss curvature
dc.subjectspace form
dc.subjectPrimary: 11C20
dc.subjectSecondary: 11E25
dc.subject53C24
dc.subject53C42
dc.titleA Note on Surfaces in Space Forms with Pythagorean Fundamental Forms
dc.typeArticle

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