In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principal, Gaussian, and mean curvatures in terms of the eigenvalues of the differential of this map. Considering planar sections containing the normal field, we also define normal curvatures at each point of the surface, and with respect to each tangent direction. We investigate the relations between these curvature types. Further on we prove that, under an additional hypothesis, a compact, connected surface without boundary whose Minkowski Gaussian curvature is constant must be a Minkowski sphere. Since existing literature on the subject of our paper is widely scattered, in the introductory part also a survey of related results is given.

中文翻译：

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三维赋范空间中浸入面的微分几何

在本文中，我们研究了三维（有范或）闵可夫斯基空间中浸入曲面的曲率类型。通过赋予表面一个法向矢量场，即由环境 Birkhoff 正交性给出的横向矢量场，我们得到了高斯图的类似物。然后我们可以根据该映射微分的特征值定义主曲率、高斯曲率和平均曲率的概念。考虑到包含法线场的平面部分，我们还定义了表面每个点的法线曲率，并相对于每个切线方向。我们研究这些曲率类型之间的关系。进一步证明，在一个附加假设下，一个密可夫斯基高斯曲率恒定的无边界连通面必定是一个闵可夫斯基球。