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Conjugate-cut loci and injectivity domains on two-spheres of revolution

Bernard BonnardJean-Baptiste CaillauGabriel Janin — 2013

ESAIM: Control, Optimisation and Calculus of Variations

In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is  = d  + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the convexity properties...

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