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

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Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
Volume:12 Issue:1
A new characterization of Aminov surface with regards to its Gauss map in E^4

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

Authors : Sezgin BÜYÜKKÜTÜK, Günay ÖZTÜRK

Pages : 25-32

Doi:10.17798/bitlisfen.1170647

View : 40 | Download : 11

Publication Date : 2023-03-22

Article Type : Conference Paper

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.
Keywords : Aminov surface, Gauss map, Monge patch

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