On the Laplace Normal Vector Field of Skew Ruled Surfaces

Stylianos Stamatakis

On the Laplace Normal Vector Field of Skew Ruled Surfaces

Differential Geometry 2016-03-16 v1

Authors: Stylianos Stamatakis

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.

Keywords

Laplace normal vector field skew ruled surfaces ruled surfaces Gaussian curvature relative normalization asymptotic plane

Cite

@article{arxiv.1510.08489,
  title  = {On the Laplace Normal Vector Field of Skew Ruled Surfaces},
  author = {Stylianos Stamatakis},
  journal= {arXiv preprint arXiv:1510.08489},
  year   = {2016}
}

Comments

appears in the Proceedings of the 1st International Workshop on Line Geometry and Kinematics (IW-LGK-11), April 26-30, 2011, Paphos, Cyprus

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