One-parameter family of Clairaut-Liouville metricsReport as inadecuate




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1 IMB - Institut de Mathématiques de Bourgogne Dijon 2 IRIT - Institut de recherche en informatique de Toulouse 3 Tokai University

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.

Keywords : $2$-sphere of revolution unfolding space mechanics





Author: Bernard Bonnard - Jean-Baptiste Caillau - Minoru Tanaka -

Source: https://hal.archives-ouvertes.fr/



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