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On projectively invariant points of an oval with a distinguished exterior line. (English. Russian original) Zbl 1390.51007
Probl. Inf. Transm. 53, No. 3, 279-283 (2017); translation from Probl. Peredachi Inf. 53, No. 3, 84-89 (2017).
Summary: 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.

MSC:
51E21 Blocking sets, ovals, \(k\)-arcs
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[1] Nikolaev, P.P., Recognition of projectively transformed planar figures. I: analysis and invariant mapping of segmented ovals, Sensornye Sistemy, 25, 118-137, (2011)
[2] Nikolaev, P.P., Recognition of projectively transformed planar figures. II: an oval in a composition with a dual element of a plane, Sensornye Sistemy, 25, 245-266, (2011)
[3] Blagojević, P.V.M.; Karasev, R.N., The Schwarz genus of the Stiefel manifold, Topology Appl., 160, 2340-2350, (2013) · Zbl 1281.55005
[4] Milnor, J.W., Morse Theory: Based on Lecture Notes by M. Spivak and R. Wells, Princeton, N.J.: Princeton Univ. Press, 1963. Translated under the title Teoriya Morsa, Moscow: Mir, 1965.
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