The inverse surfaces of tangent developables with respect to sc(r)
Abstract
In this paper, we define the inverse surface of a tangent developable surface with respect to the sphere Sc(r) with the center c∈ E3 and the radius r in 3-dimensional Euclidean space E3. 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.
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