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Article Dans Une Revue Saitama Mathematical Journal Année : 2021

Osculating spheres to a family of curves.

Résumé

The authors study the extrinsic conformal geometry of space forms involving pencils of circles or spheres. They consider curves orthogonal to a foliation of an open set of a 3-sphere by spheres and prove that the osculating spheres to the curves at points of a leaf form a pencil. They first prove the analogous result in a lower-dimensional case, that is, foliations of the 2-dimensional sphere and their orthogonal foliations. The 3-dimensional result, that is, the result for a foliation of (an open subset of) the 3-dimensional sphere by 2-dimensional spheres, is obtained using the de Sitter space, which is a model for the set of oriented spheres of the 3-dimensional sphere.
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Dates et versions

hal-03540448 , version 1 (24-01-2022)

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  • HAL Id : hal-03540448 , version 1

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Rémi Langevin, Jun O’hara, Jean-Claude Sifre. Osculating spheres to a family of curves.. Saitama Mathematical Journal, 2021, 33, pp.13-22. ⟨hal-03540448⟩
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