Geometry of the line space associated to a given dual ruled surface

Rawya A. Hussein; Ali A. Ali; Rawya A. Hussein; Ali A. Ali

doi:10.3934/math.2022476

AIMS Mathematics

2022, Volume 7, Issue 5: 8542-8557. doi: 10.3934/math.2022476

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Geometry of the line space associated to a given dual ruled surface

Rawya A. Hussein ¹,
Ali A. Ali ^{2
,
,}

1.
Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
2.
Department of Mathematics, College of Science and Arts, AlMithnab, Qassim University, Buridah 51931, Saudi Arabia

Received: 09 December 2021 Revised: 06 February 2022 Accepted: 14 February 2022 Published: 28 February 2022
MSC : 53A10, 53A25, 53C50

As a continuation to our results in ^[1], we study the dual ruled surface defined on the set of dual numbers. The idea of the dual part are defined similar to quaternion space. The dual part of this represents a ruled dual submanifold. The geometric properties of their dual parts are investigated. Some examples are given and plotted.
- line space,
- dual space,
- dual sphere,
- ruled surfaces
Citation: Rawya A. Hussein, Ali A. Ali. Geometry of the line space associated to a given dual ruled surface[J]. AIMS Mathematics, 2022, 7(5): 8542-8557. doi: 10.3934/math.2022476

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Abstract

As a continuation to our results in ^[1], we study the dual ruled surface defined on the set of dual numbers. The idea of the dual part are defined similar to quaternion space. The dual part of this represents a ruled dual submanifold. The geometric properties of their dual parts are investigated. Some examples are given and plotted.

References

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