Classification of metallic shaped hypersurfaces in real space forms

Özgür, Cıhan; Özgür, Nihal Yılmaz

doi:10.3906/mat-1408-17

Cited by 18 publications

(13 citation statements)

References 11 publications

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“…Since ∇J = 0, the last equation is reduced to M is said to be metallic shaped hypersurface in a space form N n+1 (c) if the shape operator A of M is a metallic structure (see [14]). ) sphere is a locally metallic shaped hypersurfaces in R n+1 .…”

Section: An Almost Quadratic Metricmentioning

confidence: 99%

A Neutral relation between metallic structure and almost quadratic φ -structure

Gönül¹,

Erken²,

Yazla³

et al. 2019

Turk J Math

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Section: An Almost Quadratic Metricmentioning

confidence: 99%

A Neutral relation between metallic structure and almost quadratic φ -structure

Gönül¹,

Erken²,

Yazla³

et al. 2019

Turk J Math

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“…It is worth to point out that the Pythagorean-like formula is similar to the so-called metallic shaped hypersurface equation: ( [12,13])…”

Section: Introductionmentioning

confidence: 96%

Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms

Aydın

Mihai

Özgür

2022

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We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature φ+c, where φ is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model.

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“…For example, in [19], the golden ratio is used in graphs; in [10], it is proved that in any dimension all solutions between unity and the golden ratio to the optimal spherical code problem for N spheres are also solutions to the corresponding DLP (the densed local packing problem) problem. Some geometric applications of the golden ratio and its generalizations have been used to introduce new types of manifolds (see, for example, [2], [3], [11], [13], [14] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Finite Blaschke products and the golden ratio

Özgür¹,

Uçar²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Geometric properties of …nite Blaschke products have been intensively studied by many di¤erent aspects. In this paper, our aim is to study geometric properties of …nite Blaschke products related to the golden ratio2 . Mainly, we focus on the relationships between the zeros of canonical …nite Blaschke products of lower degree and the golden ratio. We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of …nite Blaschke products.2020 Mathematics Subject Classi…cation. Primary 30J10; 11B39. Keywords and phrases. Finite Blaschke product, golden ratio, golden triangle, golden ellipse, golden

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Classification of metallic shaped hypersurfaces in real space forms

Abstract: We define the notion of a metallic shaped hypersurface and give the full classification of metallic shaped hypersurfaces in real space forms. We deduce that every metallic shaped hypersurface in real space forms is a semisymmetric hypersurface.

Cited by 18 publications

References 11 publications

A Neutral relation between metallic structure and almost quadratic φ -structure

A Neutral relation between metallic structure and almost quadratic φ -structure

Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms

Finite Blaschke products and the golden ratio

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