Sub-Finsler geometry in dimension three

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Abstract

We define the notion of sub-Finsler geometry as a natural generalization of sub-Riemannian geometry with applications to optimal control theory. We compute a complete set of local invariants, geodesic equations, and the Jacobi operator for the three-dimensional case and investigate homogeneous examples. © 2006 Elsevier B.V. All rights reserved.

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Clelland, J. N., & Moseley, C. G. (2006). Sub-Finsler geometry in dimension three. Differential Geometry and Its Application, 24(6), 628–651. https://doi.org/10.1016/j.difgeo.2006.04.005

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