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.
- 53B15, 53C17, 14M15, 17B10, 22E46, 53C15, 53C30, 58A32, 58J70, 93C10
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- Department of Mathematical Sciences - Professor
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching