A new characterization of Aminov surface with regards to its Gauss map in E^4-Reference-Cited by-同舟云学术

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

Published:2023-03-22 Issue:1 Volume:12 Page:25-32
ISSN:2147-3129
Container-title:Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
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Author:

BÜYÜKKÜTÜK Sezgin¹^ORCID,ÖZTÜRK Günay²^ORCID

Affiliation:

1. KOCAELİ ÜNİVERSİTESİ

2. İZMİR DEMOKRASİ ÜNİVERSİTESİ

Abstract

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.

Publisher

Bitlis Eren Universitesi Fen Bilimleri Dergisi

Subject

Earth-Surface Processes

Reference8 articles.

1. [1] B. Bulca, K. Arslan, " Surfaces Given with the Monge Patch in E^4 ," Journal of Mathematical Physics, Analysis, Geometry, vol. 9, pp. 435-447, 2013.

2. [2] S. Büyükkütük, G. Öztürk, "A new type timelike surface given with Monge patch in E^4 , " TWMS J. App. and Eng. Math., vol. 11, 176–183, 2021.

3. [3] B.Y. Chen, Geometry of Submanifolds. New York: Dekker, 1973.

4. [4] B.Y. Chen, M. Choi, Y.H. Kim, "Surfaces of revolution with pointwise 1-type Gauss map.," J. Korean Math. Soc. vol . 42, 447–455, 2005.

5. [5] G. Gray, "A Monge Patch.," Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton. FL: CRC Press. pp. 398–401, 1997.