Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space

Kişi, İlim; Öztürk, Günay

doi:10.36890/iejg.628083

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Theorem 16.4. [121] There exists no tubular surface M given with the parametrization (16.2) having pointwise 1-type Gauss map of the second kind which satisfies…”

Section: Euclidean Submanifolds With Pointwise 1-type Gauss Mapsmentioning

confidence: 99%

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Chen

Güler

Yaylı

et al. 2023

International Electronic Journal of Geometry

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The theory of finite type submanifolds was introduced by the first author in late 1970s and it has become a useful tool for investigation of submanifolds. Later, the first author and P. Piccinni extended the notion of finite type submanifolds to finite type maps of submanifolds; in particular, to submanifolds with finite type Gauss map. Since then, there have been rapid developments in the theory of finite type. The simplest finite type submanifolds and submanifolds with finite type Gauss maps are those which are of 1-type. The classes of such submanifolds constitute very special and interesting families in the finite type theory.

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“…Theorem 16.4. [121] There exists no tubular surface M given with the parametrization (16.2) having pointwise 1-type Gauss map of the second kind which satisfies…”

Section: Euclidean Submanifolds With Pointwise 1-type Gauss Mapsmentioning

confidence: 99%

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Chen

Güler

Yaylı

et al. 2023

International Electronic Journal of Geometry

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“…In [3,4], the authors handled Aminov surfaces according to their curvatures in − 4 dimensional Euclidean and Minkowski spaces. The other studies about some surfacesin can be found in [9,10,11,12]. In this study, we evaluate Aminov surfaces with regards to their Gauss maps in .…”

Section: Introductionmentioning

confidence: 99%

A new characterization of Aminov surface with regards to its Gauss map in E^4

Büyükkütük

Öztürk²

2023

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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In this work, we focus on Aminov surface with regard to its Gauss map in E^4. Firstly, we write the covariant derivatives according to linear combinations of orthonormal vectors and separate the equalities using Gauss and Weingarten formulas. Then, we get the laplace of the Gauss map. After giving some conditions, we yield as main results: Aminov surfaces can not have harmonic Gauss map and can not have pointwise one-type Gauss map of I. kind in E^4. Further, we give an example of helical cylinder which is also congruent to an Aminov surface. Lastly, we obtain the conditions of having pointwise one-type Gauss map of II. kind.

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“…Whether a surface has pointwise one type Gauss map is important in categorizing surfaces. In many recent studies, especially in Euclidean spaces, the Laplacian of the Gauss map has been obtained and some analyzes have been made on surfaces [3,4,5,13]. Regarding the Gauss map (G) of a surface, if the condition…”

Section: Introductionmentioning

confidence: 99%

An Investigation of Timelike Aminov Surface with respect to its Gauss Map in Minkowski Space-time

Büyükkütük

2023

International Electronic Journal of Geometry

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In this work, we handle timelike Aminov surfaces in E_1^4 with respect to having pointwise one type Gauss map. Firstly, we get the laplace of Gauss map of this type of surface. Then, we obtain that there is no timelike Aminov surface having harmonic Gauss map and also pointwise one type Gauss map of first kind in Minkowski 4-space. Further, we yield the conditions of having pointwise one type Gauss map of second kind.

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Tubular Surface Having Pointwise 1-type Gauss Map in Euclidean 4-Space

Cited by 5 publications

References 19 publications

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

Differential Geometry of 1-type Submanifolds and Submanifolds with 1-type Gauss Map

A new characterization of Aminov surface with regards to its Gauss map in E^4

An Investigation of Timelike Aminov Surface with respect to its Gauss Map in Minkowski Space-time

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