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arXiv · 1510.08489

On the Laplace Normal Vector Field of Skew Ruled Surfaces

Stylianos Stamatakis
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Abstract

We consider the Laplace normal vector field of relatively normalized ruled surfaces with non-vanishing Gaussian curvature in the three-dimensional Euclidean space $\mathbb{R}^{3}$. We determine all ruled surfaces and all relative normalizations for which the Laplace normal image degenerates into a point or into a curve. Moreover, we study the Laplace normal image of a non-conoidal ruled surface whose relative normals lie on the asymptotic plane.

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Stylianos Stamatakis. 2015-10-28. On the Laplace Normal Vector Field of Skew Ruled Surfaces. https://arxiv.org/abs/1510.08489

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