Bertrand curves and Razzaboni surfaces in Minkowski 3-space

摘要

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B"{a}cklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B"{a}cklund transformations on Razzaboni surfaces commute.