Abstract:In the homogeneous space Sol$_{3}$, a translation surface is parametrized by $r(s,t)=\gamma _{1}(s)\ast \gamma _{2}(t)$, where $\gamma _{1}$ and $\gamma _{2}$ are curves contained in coordinate planes. In this article, we study translation invariant surfaces in ${\rm Sol}_{3}$, which has finite type immersion.
Keywords: Laplacian operator; homogeneous space; invariant surface; surfaces of coordinate finite type
DOI: DOI 10.14712/1213-7243.2020.018
AMS Subject Classification: 53C30 53B25