Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2
Abstract
In the setting of step 2 sub-Finsler Carnot groups with strictly convex norms, we prove that all infinite geodesics are lines. It follows that for any other homogeneous distance, all geodesics are lines exactly when the induced norm on the horizontal space is strictly convex. As a further consequence, we show that all isometric embeddings between such homogeneous groups are affine. The core of the proof is an asymptotic study of the extremals given by the Pontryagin Maximum Principle.
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Information & Authors
Information
Published In
SIAM Journal on Control and Optimization
Pages: 447 - 461
DOI: 10.1137/19M1271166
ISSN (online): 1095-7138
Copyright
© 2020, Society for Industrial and Applied Mathematics.
History
Submitted: 27 June 2019
Accepted: 18 November 2019
Published online: 12 February 2020
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Authors
Funding Information
Academy of Finland https://doi.org/10.13039/501100002341 : 288501
Funding Information
H2020 European Research Council https://doi.org/10.13039/100010663 : 713998
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