The inverse surfaces of tangent developables with respect to s_{c}(r)

M. Evren Aydin; Mahmut Ergut

The inverse surfaces of tangent developables with respect to s_{c}(r)

Differential Geometry 2012-05-17 v1

Authors: M. Evren Aydin , Mahmut Ergut

Abstract

In this paper, we define the inverse surface of a tangent developable surface with respect to the sphere S_{c}(r) with the center $c\in \mathbb{E}^{3}$ and the radius r in 3-dimensional Euclidean space $\mathbb{E}^{3}$ . We obtain the curvatures, the Christoffel symbols and the shape operator of this inverse surface by the help of these of the tangent developable surface. Morever, we give some necessary and sufficient conditions regarding the inverse surface being flat and minimal.

Keywords

inverse surface tangent developable curvature Christoffel symbols shape operator flat surface minimal surface

Cite

@article{arxiv.1205.3561,
  title  = {The inverse surfaces of tangent developables with respect to s_{c}(r)},
  author = {M. Evren Aydin and Mahmut Ergut},
  journal= {arXiv preprint arXiv:1205.3561},
  year   = {2012}
}

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8 Pages

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