A new characterization of the Aminov surface with regards to its Gauss map in E^4
Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, cilt.12, sa.1, ss.25-32, 2023 (TRDizin)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.