Translation surfaces of coordinate finite type

2019/02/07 by Al-Zoubi, Hassan, Stamatakis, Stylianos, Al-Mashaleh, Waseem +1
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1902.03131

Abstract

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

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