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

Abstract

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.

Keywords

• Sonlu tipte yüzeyler
• Galile uzayı
• küresel çarpım yüzeyi

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

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.

Keywords

• Finite type surface
• Galilean space
• spherical product surface

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