Rotational surfaces with Cheng-Yau operator in Galilean 3-spaces

Abstract

In this paper, we study three types of rotational surfaces in Galilean 3-spaces. We classify rotational surfaces satisfying L 1 G = F (G + C) for some constant vector C ∈ G 3 and smooth function F , where L 1 denotes the Cheng-Yau operator.

Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures

“…Those surfaces were completely obtained in [12][13][14][15][16] when H and K are a constant function.…”

“…where H and K only depend on s or t and a prime denotes the derivative with respect to the related variable. The Equations ( 5)-( 8) were solved in [13,25,26] when K and H are a constant.…”

Surfaces in pseudo-Galilean space with prescribed mean curvature

“…Those surfaces in Galilean and pseudo-Galilean geometries have been considered in several research articles from different geometrical point of views. For example, the results on these surfaces in terms of Gaussian and mean curvatures can be found in [11][12][13][14][15][16][17][18][19], while the ones in terms of the Laplacian associated with the fundamental forms are in [20][21][22][23]. Some surfaces satisfying Eqn.…”

“…A surface 𝑥 = 𝑓(𝑠)𝑔(𝑡) satisfying Eqn. (1) is either a cylinder with isotropic rulings or a translation surface of the form Eqn (16),. where one generating curve is one dimensional solution to Eqn.…”