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The Inverse Surfaces Of Tangent Developables With Respect To S_c(r)

Muhittin Evren Aydin*, Mahmut ERGÜT**

*-** Department of Mathematics, Firat University, Turkey.

Periodicity:April - June'2012
DOI : https://doi.org/10.26634/jmat.1.2.1846

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 and the radius r in 3-dimensional Euclidean space 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

Inversion, Inverse surface, Developable surface, Fundamental forms, Christoffel symbols.

How to Cite this Article?

Aydin, M.E., and Ergüt, M. (2012). The Inverse Surfaces of Tangent Developables with Respect to S ( R). i-manager’s Journal on Mathematics, 1(2), 7-12. https://doi.org/10.26634/jmat.1.2.1846

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The Inverse Surfaces Of Tangent Developables With Respect To Sc(r)