arXiv subjects

Mutaz Al-Sabbagh

Publications and source records attributed to Mutaz Al-Sabbagh.

2 recordsLinked to original sources

arXiv2020

Surfaces of coordinate finite II-type

In this article, we study the class of surfaces of revolution in the 3-dimensional Euclidean space $E^{3}$ with nonvanishing Gauss curvature whose position vector $\boldsymbol{x}$ satisfies the condition $\Delta^{II}\boldsymbol{x}=A\boldsymbol{x}$, where $A$ is a square matrix of order 3 and $\Delta^{II}$ denotes the Laplace operator of the second fundamental form $II$ of the surface. We show that a surface of revolution satisfying the preceding relation is a catenoid or part of a sphere.

math.GM↗

arXiv2019

Characterization of quadric surfaces in terms of coordinate finite type Gauss map

In this article, we introduce an important class of surfaces, namely, quadrics in the Euclidean 3-space $\mathbb{E}^{3}$. We prove that planes, spheres and circular cylinders are the only quadric surfaces whose Gauss map $\boldsymbol{G}$ satisfies a relation of the form $\Delta^{I}\boldsymbol{G}= M \boldsymbol{G}$, where $M$ is a square matrix of order 3 and $\Delta^{I}$ is the Laplace-Beltrami operator corresponding to the first fundamental form $I$ of the surface.

math.GM↗