Differential geometry of general affine plane curves
In this paper we study the general affine geometry of curves in affine space A2.For a regular plane curve,we define two types of moving frames.The first is of minimal order in all moving frames.The second is the Frenet moving frame.We get the moving equations of these moving frames.We prove that curvature and signature are the complete invariants of regular curves.As an application we give a complete classification of curves with constant curvature in A2.
general affine differential geometryplane curvemoving frameinvariant arc elementcurvature
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