Some new examples of nonorientable minimal surfaces

Abstract

The classical Henneberg’s minimal surface (1875, [3, 4, 11]) was the unique nonorientable example known until 1981, when Meeks [6] exhibited the first example of a nonorientable, regular, complete, minimal surface of finite total curvature − 6 π - 6\pi . In this paper, we study the nonorientable, regular, complete minimal surfaces of finite total curvature and give some examples of punctured projective planes regularly and minimally immersed in R 3 {{\mathbf {R}}^3} and R n {{\mathbf {R}}^n} .