### AIMS Mathematics

2021, Issue 10: 11109-11123. doi: 10.3934/math.2021645
Research article

# A study on a line congruence as surface in the space of lines

• Received: 07 February 2021 Accepted: 21 July 2021 Published: 03 August 2021
• MSC : 53A04, 53A05, 53A17

• In this work, we introduce a line congruence as surface in the space of lines in terms of the E. Study map. This provides the ability to derive some formulae of surfaces theory into line spaces. In addition, the well known equation of the Plucker's conoid has been obtained and its kinematic-geometry are examined in details. At last, an example of application is investigated and explained in detail.

Citation: Rashad A. Abdel-Baky, Monia F. Naghi. A study on a line congruence as surface in the space of lines[J]. AIMS Mathematics, 2021, 6(10): 11109-11123. doi: 10.3934/math.2021645

### Related Papers:

• In this work, we introduce a line congruence as surface in the space of lines in terms of the E. Study map. This provides the ability to derive some formulae of surfaces theory into line spaces. In addition, the well known equation of the Plucker's conoid has been obtained and its kinematic-geometry are examined in details. At last, an example of application is investigated and explained in detail.

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