English

Translation surfaces of coordinate finite type

General Mathematics 2022-02-07 v1

Abstract

We consider translation surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form IIIIII, i.e. their position vector xx satisfies the relation ΔIIIx=Λx\Delta^{III}x = \Lambda x, where Λ\Lambda is a square matrix of order 3. We show that Sherk's minimal surface is the only translation surface satisfying ΔIIIx=Λx\Delta^{III}x = \Lambda x.

Keywords

Cite

@article{arxiv.1902.03131,
  title  = {Translation surfaces of coordinate finite type},
  author = {Hassan Al-Zoubi and Stylianos Stamatakis and Waseem Al-Mashaleh and Mohammed Awadallah},
  journal= {arXiv preprint arXiv:1902.03131},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1710.07619