Affiliation:
1. Department of Mathematics , Higher Normal School of Mostaganem , Mostaganem , Algeria
Abstract
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
{\mathbb{I}^{3}}
under the condition
Δ
r
i
=
λ
i
r
i
{\Delta r_{i}=\lambda_{i}r_{i}}
, where
(
r
i
)
{(r_{i})}
is the i-component function of the position vector r (
i
=
1
,
2
,
3
{i=1,2,3}
),
λ
i
∈
ℝ
{\lambda_{i}\in\mathbb{R}}
and Δ denotes the
Laplace operator.
Reference20 articles.
1. L. J. Alías, A. Ferrández and P. Lucas,
Surfaces in the 3-dimensional Lorentz–Minkowski space satisfying
Δ
x
=
A
x
+
B
\Delta x=Ax+B
,
Pacific J. Math. 156 (1992), no. 2, 201–208.
2. H. Al-Zoubi, B. Senoussi, M. Al-Sabbagh and M. Ozdemir,
The Chen type of Hasimoto surfaces in the Euclidean 3-space,
AIMS Math. 8 (2023), no. 7, 16062–16072.
3. M. E. Aydin,
A generalization of translation surfaces with constant curvature in the isotropic space,
J. Geom. 107 (2016), no. 3, 603–615.
4. M. E. Aydin, A. Erdur and M. Ergut,
Affine factorable surfaces in isotropic spaces,
TWMS J. Pure Appl. Math. 11 (2020), no. 1, 72–88.
5. M. Bekkar and B. Senoussi,
Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying
Δ
r
i
=
λ
i
r
i
\Delta r_{i}=\lambda_{i}r_{i}
,
J. Geom. 103 (2012), no. 1, 17–29.