Abstract
Confocal conics form an orthogonal net. Supplementing this net with one of the following: (1) the net of Cartesian coordinate lines aligned along the principal axes of conics, (2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, (3) the net of tangents to a conic of the confocal family, we get a planar 4-web. We show that each of these 4-webs is of maximal rank and characterize confocal conics from the web theory viewpoint.
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Acknowledgements
The author thanks A. Bobenko and W. Schief for useful discussions. This research was supported by FAPESP grant #2018/20009-6 and partially by SFB/TRR 109 “Discretization in Geometry and Dynamics”. The author also thanks the personnel of the Institute of Mathematics of Technische Universität Berlin, where this study was initiated, for their warm hospitality.
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Agafonov, S.I. Confocal conics and 4-webs of maximal rank. J. Geom. 111, 47 (2020). https://doi.org/10.1007/s00022-020-00562-3
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DOI: https://doi.org/10.1007/s00022-020-00562-3