Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

One-parameter family of Clairaut-Liouville metrics

Abstract : 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.
Complete list of metadatas
Contributor : Jean-Baptiste Caillau <>
Submitted on : Monday, February 4, 2008 - 10:41:16 PM
Last modification on : Friday, January 10, 2020 - 9:09:10 PM
Document(s) archivé(s) le : Friday, November 25, 2016 - 8:13:32 PM


Files produced by the author(s)


  • HAL Id : hal-00177686, version 2


Bernard Bonnard, Jean-Baptiste Caillau, Minoru Tanaka. One-parameter family of Clairaut-Liouville metrics. 2007. ⟨hal-00177686v2⟩



Record views


Files downloads