Singular minimal surfaces which are minimal

2020/11/19 by Aydin, Muhittin Evren, Erdur, Ayla, Ergut, Mahmut
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.10110

Abstract

In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R³ which are minimal. In fact, 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 R³. 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.

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