BERTRAND CURVES AND RAZZABONI SURFACES IN MINKOWSKI 3-SPACE
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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¨acklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B¨acklund transformations on Razzaboni surfaces commute.
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 normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B¨acklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B¨acklund transformations on Razzaboni surfaces commute.
참고문헌 (12)
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