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

BÜYÜKKÜTÜK, SEZGİN; ÖZTÜRK, Günay

doi:10.17798/bitlisfen.1170647

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

Atıf İçin Kopyala

BÜYÜKKÜTÜK S., ÖZTÜRK G.

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, cilt.12, sa.1, ss.25-32, 2023 (Hakemli Dergi)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 12 Sayı: 1
Basım Tarihi: 2023
Doi Numarası: 10.17798/bitlisfen.1170647
Dergi Adı: Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.25-32
Kocaeli Üniversitesi Adresli: Evet

Özet

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