In this work we study vertical graph surfaces invariant by parabolic screw motions with pitch $\ell >0$ and constant Gaussian curvature or constant extrinsic curvature in the product space $\mathbb H^2 \times \mathbb R$. In particular, we determine flat and extrinsically flat graph surfaces in $\mathbb H^2 \times \mathbb R$. We also obtain complete and non-complete vertical graph surfaces in $\mathbb H^2 \times \mathbb R$ with negative constant Gaussian curvature and zero extrinsic curvature.
Parabolic screw motion graph surface Gauss curvature extrinsic curvature flat surface
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 30 Nisan 2023 |
Kabul Tarihi | 2 Nisan 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 16 Sayı: 1 |