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Some classification of affine homothetical surfaces of finite type in 𝕀

  • Bendehiba Senoussi EMAIL logo
Veröffentlicht/Copyright: 3. August 2024
Journal of Applied Analysis
Aus der Zeitschrift Journal of Applied Analysis

Abstract

A Euclidean submanifold is said to be of Chen finite type if its coordinate functions are a finite sum of eigenfunctions of its Laplacian Δ. In this paper, we classify two types of affine homothetical surfaces of finite type in isotropic 3-space 𝕀 3 under the condition Δ r i = λ i r i , where ( r i ) is the i-component function of the position vector r ( i = 1 , 2 , 3 ), λ i and Δ denotes the Laplace operator.

MSC 2020: 53A40; 53C05; 53C45

Acknowledgements

The author is grateful to the referees for their valuable suggestions.

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Received: 2023-09-16
Revised: 2024-05-24
Accepted: 2024-05-29
Published Online: 2024-08-03

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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