On maps taking lines to plane curves

DOI10.1007/s40598-015-0027-1zbMath1333.14011arXiv1409.3403OpenAlexW1593248511MaRDI QIDQ258974

Vsevolod Petrushchenko, Vladlen Timorin

Publication date: 10 March 2016

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3403

zbMATH Keywords

cubic rational maplinear systems of curvesplanarization

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Rational and birational maps (14E05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Differential geometry of webs (53A60) Pencils, nets, webs in algebraic geometry (14C21)

Cites Work

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• Rectification of circles
• The algebra and geometry of Steiner and other quadratically parametrizable surfaces
• Rectification of circles and quaternions.
• Planarizations and maps taking lines to linear webs of conics
• Circles and Clifford algebras
• Diffeomorphisms taking lines to circles, and quaternionic Hopf fibrations
• On rectification of circles and an extension of Beltrami's theorem
• Circles and quadratic maps between spheres

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