A Study on the Bertrand Offsets of Timelike Ruled Surfaces in Minkowski 3-Space

This work extends some classical results of Bertrand curves to timelike ruled and developable surfaces using the E. Study map. This provides support to define two timelike ruled surfaces which are offset in the sense of Bertrand. It is proved that every timelike ruled surface has a Bertrand offset i...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 4; p. 783
Main Authors Abdel-Baky, Rashad A., Mofarreh, Fatemah
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2022
Subjects
Bertrand offsets
binormal surface
dual angle of pitch
Minkowski space
Offsets
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Summary:This work extends some classical results of Bertrand curves to timelike ruled and developable surfaces using the E. Study map. This provides support to define two timelike ruled surfaces which are offset in the sense of Bertrand. It is proved that every timelike ruled surface has a Bertrand offset if and only if an equation should be satisfied among their dual invariants. In addition, some new results and theorems concerning the developability of the Bertrand offsets of timelike ruled surfaces are gained.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14040783