Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density

Abstract

Abstract. In this paper, we obtain the weighted mean and weighted Gaussian curvatures of surfaces of revolution in Galilean 3-space with density e a 1 x 2 +a 2 y 2 +a 3 z 2 , a 1 , a 2 , a 3 ∈ R not all zero. Also, we investigate some cases of weighted minimal surfaces of revolution according to a i , i = 1, 2, 3 and weighted flat surfaces of revolution.

Non-Null Curves With Constant Weighted Curvature in Lorentz-Minkowski Plane With Density

“…For instance, a helicoidal surface of type I + with prescribed weighted mean curvature and Gaussian curvature in Minkowski 3-space and weighted minimal translation surfaces in Minkowski 3-space with density e z have been constructed in [15] and [16], respectively. In [17], weighted minimal translation surfaces in the Galilean 3-space with log-linear density has been classified and in [8], weighted minimal and weighted flat surfaces of revolution in Galilean 3-space with density e ax 2 +by 2 +cz 2 have been investigated. Now, we'll recall some basic notions about curves in Lorentz-Minkowski plane.…”