Subriemannian Metrics and the Metrizability of Parabolic Geometries
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | The Journal of Geometric Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007%2Fs12220-019-00320-1 |
| Doi | http://dx.doi.org/10.1007/s12220-019-00320-1 |
| Keywords | Bernstein-Gelfand-Gelfand resolution; Cartan geome;try; Overdetermined linear; Weyl connections PDE; Parabolic geometry; Projective metrizability; Subriemannian metrizability; |
| Description | 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. |
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