On construction of Mannheim curves with Myller configuration
Turkish Journal of Mathematics, cilt.50, sa.4, ss.613-635, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 50 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3672
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM), Academic Search Ultimate (EBSCO)
- Sayfa Sayıları: ss.613-635
- Anahtar Kelimeler: Frenet-type frame, Mannheim curve, Myller configuration, versor field
- Bilecik Şeyh Edebali Üniversitesi Adresli: Evet
Özet
In this study, our aim is to strengthen the results of the existing literature on the concept of Mannheim curves by using the natural and idysyncratic structure of Myller configuration. For this purpose, we examine Mannheim curves with Frenet-type frame in Myller configuration for Euclidean 3-space E3 and Euclidean 4-space E4. Since the classical Frenet frames in E3 and E4 are special cases of Frenet-type frames with Myller configuration in E3 and E4, and because of the special and natural structure of the Myller configuration, the Mannheim curves with Frenet frames in E3 and E4 are also special cases of the Mannheim curves with Frenet-type frames in E3 and E4. We derive several relations among the Frenet-type frame elements of Mannheim curves with Myller configuration. Subsequently, numerical examples illustrating the presented concepts are constructed, together with corresponding figures. We also introduce a new perspective that yields a fairly large family of curves for Mannheim curves with Myller configuration in E3. Indeed, this family contains several distinct special cases, and we exemplify only one of them by focusing on the most famous case, the Frenet frame. The main reason for this is that this study opens a new perspective for Mannheim curves, since the values aᵢ(s) are smooth functions and the parameter s∈ I is the arc-length parameter, where i∈{1,2,3} (and i∈{1,2,3,4} for E4). Moreover, the condition (Formula presented) defining these special functions arises from the Myller configuration in E3 (and E4). Consequently, we present several graphs illustrating the relationships between special cases and the general setting studied in this paper and in the existing literature.