Mannheim Curves in Nonflat 3-Dimensional Space Forms

作者：Zhao, Wenjing; Pei, Donghe^*; Cao, Xinyu

来源：Advances in Mathematical Physics, 2015, 2015: 319046.

DOI：10.1155/2015/319046

• BERTRAND CURVES
• NULL CURVES

We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian) and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves. We come to the conclusion that a necessary and sufficient condition is that a linear relationship with constant coefficients will exist between the curvature and the torsion of the given original curves. In the case of null curve, we reveal that there are no null Mannheim curves in the 3-dimensional de Sitter space.

• 出版日期2015
• 单位东北师范大学