BERTRAND CURVES AND RAZZABONI SURFACES IN MINKOWSKI 3-SPACE

Abstract

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 nor- mal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give Backlund trans- formations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and Backlund transformations on Razzaboni surfaces commute.