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

2 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In a recent article \cite{BCST2009}, we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is $g=\d\vp^{2}+m(\vp)\d\th^{2}$ to the period mapping of the $\vp$-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 deformation of the round sphere and to determine the convexity properties of the injectivity domains of such metrics related to applications to optimal control in space mechanics, quantum control and optimal transport.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00802078
Contributor : Jean-Baptiste Caillau <>
Submitted on : Tuesday, March 19, 2013 - 1:22:43 AM
Last modification on : Thursday, July 4, 2019 - 5:29:48 AM

### Identifiers

• HAL Id : hal-00802078, version 1

### Citation

Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin. Conjugate-cut loci and injectivity domains on two-spheres of revolution. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2013, 19 (2), pp.533-554. ⟨hal-00802078⟩

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