Conformal theory of curves with tractors
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Analysis and Applications |
| MU Faculty or unit | |
| 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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