圆环面S^(1)(R)×S^(1)(r)上的定倾曲线

Curve of constant inclination in torus S^(1)(R)×S^(1)(r)

圆环面是一类重要的旋转曲面,在曲面理论和实际应用中具有重要价值,故研究了圆环面S^(1)(R)×S^(1)(r)上的定倾曲线,即与环面中心圆周S^(1)(R)夹角为常数的曲线,并且给出了该类曲线的解析表达式。

Torus is an important kind of surface of revolution,which has important value in the theory of surfaces and in application.In the paper,we study the curve of constant inclination in torus S^(1)(R)×S^(1)(r),which has a constant angle with the central circle S^(1)(R).We establish the analytical expressions for such curves.