三维欧氏空间中的Bertrand伙伴D-曲线
Bertrand Partner D-Curves in Euclidean 3-space
摘要：
本文考虑了曲面上曲线的Bertrand曲线的概念，并通过考虑曲面上曲线的Darboux框架，定义了这类曲线为Bertrand D-曲线，给出了这类曲线的特征。我们还找到了这些曲线的测地曲率、法曲率和测地挠率之间的关系。进一步证明了Bertrand D-曲线的定义和特征在某些特殊情况下包含了Bertrand曲线的定义和特征。
英文摘要：
In this paper we consider the idea of Bertrand curves for curves lying on surfaces and by considering the Darboux frames of them we define these curves as Bertrand D-curves and give the characterizations for these curves. We also find the relations between the geodesic curvatures, the normal curvatures and the geodesic torsions of these associated curves. Furthermore, we show that the definition and the characterizations of Bertrand D-curves include those of Bertrand curves in some special cases.
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