Singular Minimal Surfaces which are Minimal

Abstract

In the present paper, we discuss the singular minimal surfaces in Euclidean 3?space ?3 which are minimal. Such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the usual condition of singular minimality by using a special semi-symmetric metric connection instead of the Levi-Civita connection on ?3. With this new connection, we prove that, besides planes, the singular minimal surfaces which are minimal are the generalized cylinders, providing their explicit equations. A trivial outcome is observed when we use a special semi-symmetric non-metric connection. Furthermore, our discussion is adapted to the Lorentz-Minkowski 3-space. © 2021, Emrah Evren KARA. All rights reserved.