论文标题
仪表空间曲线的差分几何形状
Differential geometry of spatial curves for gauges
论文作者
论文摘要
我们得出了浸入$ 3 $维的通用Minkowski空间的空间曲线的FRENET型结果和不变的结果，即在满足有限尺寸真实Banach空间的所有公理的线性空间中，除了对称型公理外。此外，我们还表征了圆柱形螺旋和此类空间中的整流曲线，并且也讨论了不变性的计算。最后，我们研究了单位球的翻译如何影响空间曲线的不变。
We derive Frenet-type results and invariants of spatial curves immersed in $3$-dimensional generalized Minkowski spaces, i.e., in linear spaces which satisfy all axioms of finite dimensional real Banach spaces except for the symmetry axiom. Further on, we characterize cylindrical helices and rectifying curves in such spaces, and the computation of invariants is discussed, too. Finally, we study how translations of unit spheres influence invariants of spatial curves.
