Çarpımsal Geometride Uzay Eğrileri ve Özel Eğri Çiftleri

Öz

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.

Anahtar Kelimeler

• Çarpımsal Eğri
• Çarpımsal İnvolüt ve çarpımsal Evolüt Eğriler
• Çarpımsal Bertrand Eğriler
• Çarpımsal eğrilik.

Space Curves and Special Curve Pairs in Multiplicative Calculus

Öz

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.

Anahtar Kelimeler

• Multiplicative Curve
• Multiplicative Involute and Multiplicative Evolute Curves
• Multiplicative Bertrand Curves
• Multiplicative Curvature

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