E3'te Adjoint Eğriler ile İlişkili Normal Yüzeyler

Year 2022, Volume: 11 Issue: 3, 779 - 783, 30.09.2022

Talat Körpınar , Ahmet Sazak

https://doi.org/10.17798/bitlisfen.1086972

Abstract

Bu çalışmada, ilişkili eğrilere bağlı olarak belirlenen yüzeyler üzerinde çalışıyoruz. Özel bir ilişkili eğri türü olan adjoint eğrilerin yardımıyla tanımlanan normal yüzeyleri inceliyoruz. Bunun için öncelikle çalıştığımız uzay olan 3 boyutlu Öklid uzayının temel denklemlerini ve adjoint eğri konusunu hatırlıyoruz. Daha sonra, bir adjoint eğrinin normal yüzeyinin birinci ve ikinci temel formlarını, asal eğriliklerini ve Gauss ve ortalama eğriliklerini hesaplayarak, bu yüzeyin karakterizasyonlarını ve ilgili bazı sonuçlar elde ediyoruz.

Keywords

Weingarten yüzey, Normal yüzey, Serret-Frenet çatı, Adjoint eğri

Normal Surfaces Associated with Adjoint Curves in E3

Abstract

In this study, we work on the surfaces determined in relation to associated curves. We study normal surfaces defined with the help of adjoint curves, a special type of associated curve. For this, we first remember the basic equations of the 3-dimensional Euclidean space, which is the space we work with, and the adjoint curve issue. Then, by computing the first and second fundamental forms, principal curvatures and Gaussian and mean curvatures of the normal surface of an adjoint curve, we obtain the characterizations of this surface and related some results.

Keywords

Weingarten surface, Normal surface, Serret-Frenet frame, Adjoint curve

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