On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces

Maryam T. Aldossary; Rashad A. Abdel-Baky; Maryam T. Aldossary; Rashad A. Abdel-Baky

doi:10.3934/math.2022983

AIMS Mathematics

2022, Volume 7, Issue 10: 17843-17858. doi: 10.3934/math.2022983

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Research article

On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces

Maryam T. Aldossary ¹,
Rashad A. Abdel-Baky ^{2
,
,}

1.
Department of Mathematics, College of Science, Imam Abdulrahman bin Faisal University, P.O. Box-1982, 31441 Damam, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Assiut, 71516 Assiut, Egypt

Received: 05 May 2022 Revised: 23 June 2022 Accepted: 13 July 2022 Published: 03 August 2022
MSC : 53A04, 53A05, 53A17

In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled and developable surfaces. It is proved that, every spacelike ruled surface have a Bertrand offset if and only if an equation should be fulfilled among their dual integral invariants. Consequently, some new relationships and theorems for the developability of the Bertrand offsets of spacelike ruled surfaces are outlined.
- E. Study map,
- Bertrand offsets,
- striction curves
Citation: Maryam T. Aldossary, Rashad A. Abdel-Baky. On the Blaschke approach of Bertrand offsets of spacelike ruled surfaces[J]. AIMS Mathematics, 2022, 7(10): 17843-17858. doi: 10.3934/math.2022983

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Abstract

In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike ruled and developable surfaces. It is proved that, every spacelike ruled surface have a Bertrand offset if and only if an equation should be fulfilled among their dual integral invariants. Consequently, some new relationships and theorems for the developability of the Bertrand offsets of spacelike ruled surfaces are outlined.

References

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