JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 13-20.doi: 10.6040/j.issn.1671-9352.0.2023.453

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Ruled surfaces in four-dimensional Euclidean space and their structural functions

QU Ruixiang, TIAN Hanyu, YU Yanhua*   

  1. School of Science, Northeastern University, Shenyang 110819, Liaoning, China
  • Published:2025-07-25

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Abstract: In four-dimensional Euclidean space, utilizing the definition of a waist curve, the structure functions of ruled surfaces is proposed, extending the non-developable ruled surfaces and their standard equations in three-dimensional Euclidean space to four-dimensional Euclidean space. By studing the properties of the surface itself through the structural function of the ruled surface, the relationships between the structural functions, directors, and waist curves of four types of special associated ruled surfaces are obtained, and these four kinds of ruled surfaces are classified. Finally, specific expressions for the structural functions are given when the director is a Mannheim curve and a skew helix of the third type, and the mean curvature vector field of the associated ruled surface in these cases is calculated.

Key words: four-dimensional Euclidean space, ruled surface, structure function, mean curvature, special curve

CLC Number: 

  • O185
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