Conformal theory of curves with tractors

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Authors

ŠILHAN Josef ŽÁDNÍK Vojtěch

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Mathematical Analysis and Applications
MU Faculty or unit

Faculty of Science

Citation
Web https://www.sciencedirect.com/science/article/abs/pii/S0022247X18310771
Doi http://dx.doi.org/10.1016/j.jmaa.2018.12.038
Keywords Conformal geometry; Tractor calculus; Curves; Invariants
Description We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a specification of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The absolute conformal invariants are defined via a tractor analogue of the classical Frenet frame construction and then expressed in terms of relative ones. Our approach applies likewise to conformal structures of any signature; in the case of indefinite signature we focus especially on the null curves. It also provides a conceptual tool for handling distinguished families of curves (conformal circles and conformal null helices) and conserved quantities along them.
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