A Classification Theorem for Complete PMC Surfaces with Non-negative Gaussian Curvature in $M^n(c) \times \mathbb{R}$
A Classification Theorem for Complete PMC Surfaces with Non-negative Gaussian Curvature in $M^n(c) \times \mathbb{R}$
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 …