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Differential geometry of spatial curves for gauges
Vitor Balestro, Horst Martini, Makoto Sakaki
We derive Frenet-type results and invariants of spatial curves immersed in -dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite d…
Curvature types of planar curves for gauges
Vitor Balestro, Horst Martini, Makoto Sakaki
In this paper results from the differential geometry of curves are extended from normed planes to gauge planes which are obtained by neglecting the symmetry axiom. Based on the gau…
On curvature of surfaces immersed in normed spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
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…
Some topics in differential geometry of normed spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts…
Surface immersions in normed spaces from the affine point of view
Vitor Balestro, Horst Martini, Ralph Teixeira
The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We end…
Differential geometry of immersed surfaces in three-dimensional normed spaces
Vitor Balestro, Horst Martini, Ralph Teixeira
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 transv…