# 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.
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Cited literature [10 references]

https://hal.archives-ouvertes.fr/hal-00177686
Contributor : Jean-Baptiste Caillau <>
Submitted on : Monday, September 8, 2008 - 2:26:26 PM
Last modification on : Thursday, March 26, 2020 - 6:28:41 PM
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• HAL Id : hal-00177686, version 3

### Citation

Bernard Bonnard, Jean-Baptiste Caillau, Minoru Tanaka. One-parameter family of Clairaut-Liouville metrics. 2007. ⟨hal-00177686v3⟩

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