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arXiv · 1805.00422

Conformal theory of curves with tractors

Josef Šilhan·Vojtěch Žádník
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Abstract

We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination 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. This 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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Josef Šilhan, Vojtěch Žádník. 2018-05-01. Conformal theory of curves with tractors. https://arxiv.org/abs/1805.00422

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