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Journals / Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2021 / Cilt: 23 Sayı: 2

Spherical product surfaces satisfying $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ in $\G_{3}$

$G_{3}$'te $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ şartını sağlayan küresel çarpım yüzeyleri

Bengü Bayram(BALIKESİR ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-1237-5892
Özgün Biçgin(BALIKESİR ÜNİVERSİTESİ)0000-0003-0255-8633
Pages
653–672
Publication Date
2021-07-04
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AI Summary & Key Takeaways

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

We also give exact classification of these type surfaces.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For an isometric immersion of n-dimensional connected manifold into Euclidean m-space, the position vector of M can be decomposed as a finite sum of Em valued non-constant functions of the Laplacian operator, one can say that M is of finite type.
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Key Findings & Data:In this study, we consider the spherical product surface in 3-dimensional Galilean space satisfying the condition $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ where $\Delta ^{II}$ is the Laplacian with respect to second fundamental form.
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Conclusion & Impact:We also give exact classification of these type surfaces.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sonlu tipte yüzeyler · Galile uzayı · küresel çarpım yüzeyi

Abstract

For an isometric immersion of n-dimensional connected manifold into Euclidean m-space, the position vector of M can be decomposed as a finite sum of Em valued non-constant functions of the Laplacian operator, one can say that M is of finite type. Finite type surfacas corresponds to the fundamental forms are studied in different spaces by many authors. In this study, we consider the spherical product surface in 3-dimensional Galilean space satisfying the condition $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ where $\Delta ^{II}$ is the Laplacian with respect to second fundamental form. We also give exact classification of these type surfaces.

Özet

n-boyutlu bağlantılı bir manifolddan m-boyutlu Öklid uzayına tanımlı bir izometrik daldırma için, M manifoldunun yer vektörü Laplas operatörünün sabit olmayan öz fonksiyonlarının sonlu bir toplamı olarak ayrışabiliyorsa, M manifoldu sonlu tiptedir, denir. Sonlu tipte yüzeyler farklı uzaylarda birçok yazar tarafından çalışılmıştır. Bu çalışmada, 3-boyutlu Galile uzayında, $\Delta ^{II}$ ikinci temel forma göre Laplas operatörü olmak üzere $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ eşitliğini sağlayan küresel çarpım yüzeylerini ele aldık. Ayrıca, bu yüzeylerin tam bir sınıflandırmasını verdik.

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Cite This Article

Bayram, B., Biçgin, Ö. (2021). Spherical product surfaces satisfying $\Delta ^{II}x_{i}=\lambda _{i}x_{i}$ in $\G_{3}$. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 23 Sayı: 2, 653–672. https://doi.org/10.25092/baunfbed.854728

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