Conformal theory of curves with tractors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Silhan, Josef¹  Zadnik, Vojtech² 

[1] Masaryk Univ, Inst Math & Stat, Kotlarska 2, CS-61137 Brno, Czech Republic

[2] Masaryk Univ, Fac Educ, Porici 31, Brno 60300, Czech Republic

关键词: Conformal geometry;    Tractor calculus;    Curves;    Invariants;   

DOI  :  10.1016/j.jmaa.2018.12.038

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free