Linear structures on the collections of minimal surfaces inℝ 3 andℝ 4

The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

“…So far, we find surfaces E 1 and E 2 . By using E 3 − E 5 , e 3 − e 5 , and also (12), (13), we obtain the following surfaces: E m (u, v) = (a, b, c):…”

“…There are many classical and modern minimal surfaces in the literature. See Darboux [1,2], Dierkes [3], Fomenko and Tuzhilin [4], Gray, Salamon, and Abbena [5], Nitsche [6], Osserman [7], Spivak [8] for some books, Lie [9], Schwarz [10], Small [11,12], and Weierstrass [13,14] for some papers related to minimal surfaces in Euclidean geometry.…”

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

“…There are many classical and modern minimal surfaces in the literature. See [1][2][3][4][5][6][7][8][9] for some books, [10][11][12][13][14] for some papers related to minimal surfaces in E 3 , and also [15] for those in E 4 .…”

Implicit Equations of the Henneberg-Type Minimal Surface in the Four-Dimensional Euclidean Space

“…A minimal surface in the three-dimensional Euclidean space E 3 , also in higher dimensions, is a regular surface for which the mean curvature vanishes identically. See [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] for details. On the other hand, a Henneberg surface [4][5][6], also obtained by the Weierstrass representation [8,9] is well-known classical minimal surface in E 3 .…”