6533b7d7fe1ef96bd1268c48

RESEARCH PRODUCT

One-parameter family of Clairaut-Liouville metrics

Bernard BonnardJean-baptiste CaillauMinoru Tanaka

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]space mechanics49K15 53C20 70Q05$2$-sphere of revolution[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Mathematics::Differential Geometryunfolding

description

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.

yearjournalcountryeditionlanguage
2007-09-01
https://hal.science/hal-00177686v3