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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2016 / Cilt: 16 - Sayı: 2

Classification Results on Surfaces in The Isotropic 3-Space

Anahtar kelimeler İzotropik uzay; Helikoidal yüzey; İzotropik ortalama eğrilik; Relatif eğrilik; Jeodezik; Asimptotik eğri.

Muhittin Evren AYDIN
Pages
239–246
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In particular, we classify the helicoidal surfaces in ? with constant curvature and analyze some special curves on these.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The isotropic 3-space ?? which is one of the Cayley-Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance.
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Key Findings & Data:In the present paper, we give several classifications on the surfaces in ?? with constant relative curvature (analogue of the Gaussian curvature) and constant isotropic mean curvature.
💡
Conclusion & Impact:In particular, we classify the helicoidal surfaces in ? with constant curvature and analyze some special curves on these.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The isotropic 3-space ?? which is one of the Cayley-Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in ?? with constant relative curvature (analogue of the Gaussian curvature) and constant isotropic mean curvature. In particular, we classify the helicoidal surfaces in ? with constant curvature and analyze some special curves on these.

Özet

İzotropik 3-uzay ?? Cayley-Klein uzaylarından biridir ve Öklidyen uzayda standart Öklidyen uzaklık ile izotropik uzaklığın değişiminden elde edilir. Bu çalışmada, ?? uzayında, sabit relatif (izotropik Gauss) ve sabit izotropik ortalama eğrilikli yüzeyler üzerine çeşitli sınıflandırmalar ifade edilmiştir. Özel olarak, ?? uzayında sabit eğrilikli helikoidal yüzeyler sınıflandırılıp, bu yüzeyler üzerinde bazı özel eğriler analiz edilmiştir.

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Cite This Article

AYDIN, M. E. (2022). Classification Results on Surfaces in The Isotropic 3-Space. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 16 - Sayı: 2, 239–246. https://ajindex.com/articles/430225

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