This paper investigates the hanging chain problem in the simply isotropic plane and its 2-
dimensional analog in the simply isotropic space. The simply isotropic plane and space are …

It is known that minimal surfaces in Euclidean space can be represented in terms of
holomorphic functions. For example, we have the well-known Weierstrass representation …

We study surfaces with a constant ratio of principal curvatures in Euclidean and simply
isotropic geometries and characterize rotational, channel, ruled, helical, and translational …

ZERO MEAN CURVATURE SURFACES IN ISOTROPIC THREE-SPACE 1. Introduction We
became interested in the geometry of the simply isotrop Page 1 Bull. Korean Math. Soc. 58 (2021) …

We consider the extrinsic geometry of surfaces in simply isotropic space, a three-
dimensional space equipped with a rank 2 metric of index zero. Since the metric is …

In this paper, we investigate surfaces in singular semi-Euclidean space $\mathbb {R}^{0, 2,
1} $ endowed with a degenerate metric. We define $ d $-minimal surfaces, and give a …

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 …

In this paper, we classify warped translation surfaces being invariant surfaces of i-type, that
is, the generating curve has formed by the intersection of the surface with the isotropic xz …

In this paper, we classify parabolic revolution surfaces in the three-dimensional simply
isotropic space 𝕀 3 under the condition Δ J xi= λ ixi, J= I, II, where Δ J is the Laplace operator …

We study some submanifolds in pseudo-Riemannian space forms in terms of the
degeneracy, which means that metrics on manifolds are degenerate. More precisely, via d …