One-parameter family of Clairaut-Liouville metrics
Résumé
Riemannian metrics with singularities are considered on the $2$-sphere of revolution. The analysis of such singularities is motivated by examples stemming from mechanics and related to projections of higher dimensional (regular) sub-Riemannian distributions. An unfolding of the metrics in the form of an homotopy from the canonical metric on $\SS^2$ is defined which allows to analyze the singular case as a limit of standard Riemannian ones. A bifurcation of the conjugate locus for points on the singularity is finally exhibited.
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
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