三维仿射空间中曲线的性质

Curve Characterization in 3D Affine Space

研究了三维仿射空间中曲线的结构方程,讨论了半Euclid空间中空间曲线的不变量.通过考虑一条既在三维欧几里空间又在三维闵可夫斯基空间中的空间曲线,得出三维仿射空间中与曲率、挠率及转动惯量有关的两个不变量,并证明了这两个不变量与环绕空间的度量选取无关.

The structure equations of curves were studied in 3D affine space,and the invariants of space curves were discussed in the semi Euclid space.A space curve that is both in 3D Euclid space and 3D Minkowski space was considered,and two invariants were obtained which are curvature,torsion and moment of inertia dependent.It was verified that the two invariants are independent of the choice of inner products.