Variations on the Tait-Kneser theorem

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The classical Tait-Kneser theorem states that the osculating circles of a smooth plane curve, free from curvature extrema, are pairwise disjoint. We prove a number of analogs of this theorem, e.g., for ovals of osculating cubics, osculating polynomials and trigonometric polynomials; in each case, we will obtain a non-differentiable foliation with smooth leaves.
14 pages, 6 figures, v2: references added

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Differential Geometry, Algebraic Geometry, 53A20; 51N15

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http://salesiana.dossiersoluciones.com/handle/123456789/108970

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602317
 http://arxiv.org/abs/math/0602317

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arXiv