Abstract
Let $M^{n}(c)$ be an $n$-dimensional space form with constant sectional curvature $c$. Alencar-do Carmo-Tribuzy [5] classified all parallel mean curvature (abbrev. PMC) surfaces with non-negative Gaussian curvature $K$ in $M^n(c) \times \mathbb{R}$ with $c \lt 0$. Later on, Fetcu-Rosenberg [28] generalized their results for $c \neq 0$. However, the classification to PMC surfaces in $M^n(c) \times \mathbb{R}$ with $K \equiv 0$ is still open. In this paper, we give a complete classification to the PMC surfaces in $M^n(c) \times \mathbb{R}$ with $K \equiv 0$ whose tangent plane spans the constant angle with factor $\mathbb{R}$.
Citation
Zhong Hua Hou. Wang Hua Qiu. "A Classification Theorem for Complete PMC Surfaces with Non-negative Gaussian Curvature in $M^n(c) \times \mathbb{R}$." Taiwanese J. Math. 20 (1) 205 - 226, 2016. https://doi.org/10.11650/tjm.20.2016.5766
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