Differential geometry of immersed surfaces in three-dimensional normed spaces

@article{Balestro2020DifferentialGO,
  title={Differential geometry of immersed surfaces in three-dimensional normed spaces},
  author={Vitor Balestro and Horst Martini and Ralph Teixeira},
  journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  year={2020},
  volume={90},
  pages={111-134}
}
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… 

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The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given by an arbitrary

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Some topics in differential geometry of normed spaces

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