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摘要
A translation surface in Euclidean space is a surface that is the sum of two regular curves alpha and beta In this paper we characterize all minimal translation surfaces. In the case that alpha and beta are non-planar curves, we prove that the curvature and the torsion tau of both curves must satisfy the equation k(2)tau = C where C is constant. We show that, up to a rigid motion and a dilation in the Euclidean space and, up to reparametrizations of the curves generating the surfaces, all minimal translation surfaces are described by two real parameters a, b is an element of R where the surface is of the form phi(s, t) = beta(a,b) (s) + beta a,b(t).
- 出版日期2017-10
