Geodesic
Translation surfaces of finite type in ${\rm Sol}_{3}$
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 237-256.

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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.
DOI : 10.14712/1213-7243.2020.018
Classification : 53B25, 53C30
Keywords: Laplacian operator; homogeneous space; invariant surface; surfaces of coordinate finite type 
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Senoussi, Bendehiba; Al-Zoubi, Hassan. Translation surfaces of finite type in ${\rm Sol}_{3}$. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 2, pp. 237-256. doi : 10.14712/1213-7243.2020.018. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.018/

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