BERTRAND CURVES AND RAZZABONI SURFACES IN MINKOWSKI 3-SPACE | Zendy

XU Chuan-you | Zendy; Xifang Cao | Zendy; Peng Zhu | Zendy

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BERTRAND CURVES AND RAZZABONI SURFACES IN MINKOWSKI 3-SPACE

Author(s) -

XU Chuan-you,

Xifang Cao,

Peng Zhu

Publication year - 2015

Publication title -

bulletin of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.295

H-Index - 27

eISSN - 2234-3016

pISSN - 1015-8634

DOI - 10.4134/bkms.2015.52.2.377

Subject(s) - minkowski space , mathematics , reciprocal , space (punctuation) , euclidean geometry , transformation (genetics) , pure mathematics , mathematical analysis , mathematical physics , geometry , philosophy , linguistics , biochemistry , chemistry , gene

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.

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