On dual surfaces in Galilean 3-space

[摘要] In the present paper, we describe dual translation surfaces in the Galilean 3-space having the constant Gaussian and mean curvatures as well as Weingarten and linear Weingarten dual translation surfaces. We also study dual translation surfaces in $ \mathbb{G}_{3} $ under the condition $ \Delta ^{II}r = \lambda _{i}r_{i} $, where $ \lambda _{i}\in R $ and $ \Delta ^{II} $ denotes the Laplacian operator respect to the second fundamental form.

[学科分类] 地球科学(综合)

[关键词] dual surfaces;dual translation surfaces;Galilean 3-space;LN-surfaces;translation surfaces