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Journals / Fırat Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 38 Sayı: 2

Space Curves and Special Curve Pairs in Multiplicative Calculus

Çarpımsal Geometride Uzay Eğrileri ve Özel Eğri Çiftleri

Hasan Es(GAZİ ÜNİVERSİTESİ, GAZİ EĞİTİM FAKÜLTESİ)0000-0002-7732-8173
Pages
81–92
Publication Date
2026-09-30
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AI Summary & Key Takeaways

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

As a particular case of the proposed theory, the three-dimensional multiplicative space is investigated, where the corresponding definitions, principal results, characterization theorems, and fundamental properties of multiplicative involute–evolute curves and Bertrand curve pairs are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the concept of multiplicative curves is developed in n-dimensional multiplicative space.
📊
Key Findings & Data:A multiplicative Serret–Frenet frame is constructed for these curves, multiplicative curvature functions are introduced, and their fundamental properties are established through several theorems.
💡
Conclusion & Impact:As a particular case of the proposed theory, the three-dimensional multiplicative space is investigated, where the corresponding definitions, principal results, characterization theorems, and fundamental properties of multiplicative involute–evolute curves and Bertrand curve pairs are presented.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Çarpımsal Eğri · Çarpımsal İnvolüt ve çarpımsal Evolüt Eğriler · Çarpımsal Bertrand Eğriler

Abstract

In this paper, the concept of multiplicative curves is developed in n-dimensional multiplicative space. A multiplicative Serret–Frenet frame is constructed for these curves, multiplicative curvature functions are introduced, and their fundamental properties are established through several theorems. Furthermore, the notions of multiplicative involute–evolute curves and multiplicative Bertrand curve pairs are formulated within the n-dimensional framework. As a particular case of the proposed theory, the three-dimensional multiplicative space is investigated, where the corresponding definitions, principal results, characterization theorems, and fundamental properties of multiplicative involute–evolute curves and Bertrand curve pairs are presented.

Özet

Bu çalışmada, n-boyutlu çarpımsal uzayda çarpımsal eğri kavramı tanımlanmış, bu eğriler için çarpımsal Serret–Frenet çatısı oluşturulmuş ve çarpımsal eğrilikler tanımlanarak bunlara ilişkin temel teoremler verilmiştir. Ayrıca, n-boyutlu çarpımsal uzayda involüt–evolüt eğrileri ile Bertrand eğri çiftleri tanımlanmıştır. Bunun yanı sıra, geliştirilen genel kuramın özel bir durumu olarak üç boyutlu çarpımsal uzay incelenmiş; ilgili tanımlar yapılmış, temel sonuçlar elde edilmiş ve involüt–evolüt eğrileri ile Bertrand eğri çiftlerine ilişkin karakterizasyonlar ve teoremler sunulmuştur.

🔖

Cite This Article

Es, H. (2026). Space Curves and Special Curve Pairs in Multiplicative Calculus. Fırat Üniversitesi Fen Bilimleri Dergisi, Cilt: 38 Sayı: 2, 81–92. https://doi.org/10.66605/fufbd.1937289

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