Minimal Translation Surfaces in Euclidean Space
Minimal Translation Surfaces in Euclidean Space
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DOI：
10.1007/s12220-017-9788-1
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
R. López;O. Perdomo
中科院分区：
文献类型：
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作者：
R. López;O. Perdomo
A translation surface in Euclidean space is a surface that is the sum of two regular curvesand. In this paper we characterize all minimal translation surfaces. In the case thatandare non-planar curves, we prove that the curvatureand the torsionof both curves must satisfy the equationwhereCis 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 parameterswhere the surface is of the form.
