caa a22 4500 445813229 CHVBK 20180317145218.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00022-011-0068-0 doi (NATIONALLICENCE)springer-10.1007/s00022-011-0068-0 Langer Joel Department of Mathematics, Case Western Reserve University, 44106-7058, Cleveland, OH, USA aut On meromorphic parameterizations of real algebraic curves [Elektronische Daten] [Joel Langer] A singular flat geometry may be canonically assigned to a real algebraic curve Γ; namely, via analytic continuation of unit speed parameterization of the real locus $${\Gamma_\mathbb{R}}$$ . Globally, the metric $${\rho=|Q|=|q(z)|dzd\bar{z}}$$ is given by the meromorphic quadratic differential Q on Γ induced by the standard complex form dx 2+dy 2 on $${\mathbb{C}^2=\{(x,y)\}}$$ . By considering basic properties of Q, we show that the condition for local arc length parameterization along $${\Gamma_\mathbb{R}}$$ to extend meromorphically to the complex plane is quite restrictive: For curves of degree at most four, only lines, circles and Bernoulli lemniscates have such meromorphic parameterizations. Springer Basel AG, 2011 Real algebraic curve nationallicence meromorphic quadratic differential nationallicence Bernoulli lemniscate nationallicence arc length parameterization nationallicence Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 105-128 0047-2468 100:1-2<105 2011 100 22 https://doi.org/10.1007/s00022-011-0068-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00022-011-0068-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Langer Joel Department of Mathematics, Case Western Reserve University, 44106-7058, Cleveland, OH, USA aut NATIONALLICENCE 773 0- Journal of Geometry SP Birkhäuser Verlag Basel 100/1-2(2011-04-01), 105-128 0047-2468 100:1-2<105 2011 100 22 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer