Email this article On projectively invariant points of an oval with a distinguished exterior line
- Authors: Balitskii A.M.1,2, Savchik A.V.1, Gafarov R.F.3, Konovalenko I.A.1
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Affiliations:
- Kharkevich Institute for Information Transmission Problems
- Moscow Institute of Physics and Technology
- Innopolis University
- Issue: Vol 53, No 3 (2017)
- Pages: 279-283
- Section: 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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Abstract
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.
About the authors
A. M. Balitskii
Kharkevich Institute for Information Transmission Problems; Moscow Institute of Physics and Technology
Author for correspondence.
Email: alexey_m39@mail.ru
Russian Federation, Moscow; Moscow
A. V. Savchik
Kharkevich Institute for Information Transmission Problems
Email: alexey_m39@mail.ru
Russian Federation, Moscow
R. F. Gafarov
Innopolis University
Email: alexey_m39@mail.ru
Russian Federation, Innopolis, Republic of Tatarstan
I. A. Konovalenko
Kharkevich Institute for Information Transmission Problems
Email: alexey_m39@mail.ru
Russian Federation, Moscow
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