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Convexity of injectivity domains on the ellipsoid of revolution: The oblate case

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Geometrie riemannienne Convexity of injectivity domains on the ellipsoid of revolution: The oblate case Bernard Bonnard a, Jean-Baptiste Caillau a and Ludovic Rifford b aInstitut math., Univ. Bourgogne & CNRS, 9 avenue Savary, F-21078 Dijon bLabo. Dieudonne, Univ. Nice & CNRS, Parc Valrose, F-06108 Nice Received *****; accepted after revision +++++ Presented by Abstract We characterize the convexity properties of the tangent injectivity domain on an the ellipsoid of revolution in the oblate case. To cite this article: Bonnard, B.; Caillau, J.-B.; Rifford, L. C. R. Acad. Sci. Paris, Ser. I xxx (200x). Resume Convexite des domaines d'injectivite sur l'ellipsoıde de revolution : le cas oblat. On caracterise les proprietes de convexite du domaine d'injectivite sur un ellipsoıde de revolution oblat. Pour citer cet article : Bonnard, B. ; Caillau, J.-B. ; Rifford, L. C. R. Acad. Sci. Paris, Ser. I xxx (200x). 1. Introduction The purpose of the present note is to study convexity properties of injectivity domains on the oblate ellipsoid of revolution given in R3 by the cartesian equation Eµ : x 2 + y2 + ( z µ )2 = 1, with unit semi-major axis and semi-minor axis of length µ ? (0,1].

  • also related

  • x? p2?

  • constant sign curvature

  • revolution

  • enough semi-minor

  • small enough

  • oblate ellipsoid


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Geometrieriemannienne
Convexity of injectivity domains on the ellipsoid of revolution: The oblate case a ab Bernard Bonnard, Jean-Baptiste Caillauand Ludovic Rifford a Institut math., Univ. Bourgogne & CNRS, 9 avenue Savary, F-21078 Dijon b Labo.Dieudonne,Univ.Nice&CNRS,ParcValrose,F-06108Nice Received *****; accepted after revision +++++ Presented by
Abstract We characterize the convexity properties of the tangent injectivity domain on an the ellipsoid of revolution in the oblate case. To cite this article: Bonnard, B.; Caillau, J.-B.; Rifford, L. C. R. Acad. Sci. Paris, Ser. I xxx (200x). Resume Convexitedesdomainesdinjectivitesurlellipsoıdederevolution:lecasoblat.tacisereseloppreirsetocedxevntieOcnra dudomainedinjectivitesurunellipsoıdederevolutionoblat.Pour citer cet article : Bonnard, B. ; Caillau, J.-B. ; Rifford, L. C. R. Acad. Sci. Paris, Ser. I xxx (200x).
1. Introduction
The purpose of the present note is to study convexity properties of injectivity domains on the oblate ellipsoid of 3 revolution given inRby the cartesian equation   2 z 2 2 Eµ:x+y+ =1, µ with unit semi-major axis and semi-minor axis of lengthµ(0,1]. To this aim, we use the covering ofEµminus its poles R×(0,π)3(θ,ϕ)7(sinϕcosθ,sinϕsinθ,µcosϕ),
Email addresses:bernard.bonnard@u-bourgogne.fr(Bernard Bonnard), (Jean-Baptiste Caillau),ludovic.rifford@math.cnrs.fr(Ludovic Rifford).
Preprint submitted to Elsevier Science
jean-baptiste.caillau@u-bourgogne.fr
October 18, 2010