In Euclidean space, we investigate surfaces whose mean curvature H satisfies the equation $$H=\alpha \langle N,{\mathbf {x}}\rangle +\lambda $$ H = α ⟨ N , x ⟩ + λ ,… Click to show full abstract
In Euclidean space, we investigate surfaces whose mean curvature H satisfies the equation $$H=\alpha \langle N,{\mathbf {x}}\rangle +\lambda $$H=α⟨N,x⟩+λ, where N is the Gauss map, $${\mathbf {x}}$$x is the position vector, and $$\alpha $$α and $$\lambda $$λ are two constants. There surfaces generalize self-shrinkers and self-expanders of the mean curvature flow. We classify the ruled surfaces and the translation surfaces, proving that they are cylindrical surfaces.
