In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions. In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions. In the last one, we discover a one-parameter family when both curvatures of these surfaces are zero; however, we find a two-parameter family when either one of those curvatures is zero. Also, we support them with examples.
Helicoidal surface extrinsic curvature conformally flat pseudo-space conformally flat pseudo-metric
Birincil Dil | İngilizce |
---|---|
Konular | Temel Matematik (Diğer) |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 30 Eylül 2023 |
Gönderilme Tarihi | 15 Haziran 2023 |
Kabul Tarihi | 13 Eylül 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 3 |