论文标题
最小的奇异最小表面
Singular minimal surfaces which are minimal
论文作者
论文摘要
在本文中，我们讨论了最小的欧几里得3空间r^{3}中的奇异最小表面。实际上，这样的表面不过是平面，一个微不足道的结果。但是，当我们通过使用特殊的半对称度量连接而不是r^{3}上的levi-civita连接来修改奇异最小值的常规条件时，获得了非平凡的结果。通过这种新的联系，我们证明，除了平面外，最小的奇异最小表面是广义圆柱体，提供了明确的方程式。当我们使用特殊的半对称性非金属连接时，会观察到微不足道的结果。此外，我们的讨论适用于Lorentz-Minkowski 3空间。
In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R^{3} 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 R^{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.
