Slice-polynomial functions and twistor geometry of ruled surfaces in $$\mathbb {CP}^3$$CP3

@article{Altavilla2017SlicepolynomialFA,
  title={Slice-polynomial functions and twistor geometry of ruled surfaces in \$\$\mathbb \{CP\}^3\$\$CP3},
  author={Amedeo Altavilla and Giulia Sarfatti},
  journal={Mathematische Zeitschrift},
  year={2017},
  volume={291},
  pages={1059-1092}
}
In the present paper we introduce the class of slice-polynomial functions: slice regular functions defined over the quaternions, outside the real axis, whose restriction to any complex half-plane is a polynomial. These functions naturally emerge in the twistor interpretation of slice regularity introduced in Gentili et al. (J Eur Math Soc 16(11):2323–2353, 2014) and developed in Altavilla (J Geom Phys 123:184–208, 2018). To any slice-polynomial function P we associate its companion$$P^\vee $$P… 
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