On projectively invariant points of an oval with a distinguished exterior line

A. M. Balitskii; A. V. Savchik; R. F. Gafarov; I. A. Konovalenko

doi:10.1134/S0032946017030097

On projectively invariant points of an oval with a distinguished exterior line

作者: Balitskii A.M.¹^,2, Savchik A.V.¹, Gafarov R.F.³, Konovalenko I.A.¹
隶属关系:
1. Kharkevich Institute for Information Transmission Problems
2. Moscow Institute of Physics and Technology
3. Innopolis University
期: 卷 53, 编号 3 (2017)
页面: 279-283
栏目: Large Systems
URL: https://journal-vniispk.ru/0032-9460/article/view/166425
DOI: https://doi.org/10.1134/S0032946017030097
ID: 166425

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详细

We consider projectively invariant points of an oval with a distinguished exterior line. For this, we introduce a projectively invariant transformation of the line parametrized by the oval. Projectively invariant points are defined as fixed points of this transformation applied twice. We prove that there are at least four such points. For the proof we reduce the problem to an affine problem and construct an extremal area parallelogram circumscribed around the oval.