Subriemannian Metrics and the Metrizability of Parabolic Geometries

• Autoři: CALDERBANK David M. J.; SLOVÁK Jan; SOUČEK Vladimír
• Rok publikování: 2021
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: The Journal of Geometric Analysis
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://link.springer.com/article/10.1007%2Fs12220-019-00320-1
• Doi: http://dx.doi.org/10.1007/s12220-019-00320-1
• Klíčová slova: Bernstein-Gelfand-Gelfand resolution; Cartan geome;try; Overdetermined linear; Weyl connections PDE; Parabolic geometry; Projective metrizability; Subriemannian metrizability
• Popis: We present the linearized metrizability problem in the context of parabolic geometries and subriemannian geometry, generalizing the metrizability problem in projective geometry studied by R. Liouville in 1889. We give a general method for linearizability and a classification of all cases with irreducible defining distribution where this method applies. These tools lead to natural subriemannian metrics on generic distributions of interest in geometric control theory.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku