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Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds

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Abstract

This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a 3-dimensional CR compact manifold locally conformally CR equivalent to the unit sphere \(\mathbb{S}^{3}\) of ℂ2. Due to Kazdan–Warner type obstructions, conditions on the function H to be realized as a Webster scalar curvature have to be given. We prove new existence results based on a new type of Euler–Hopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal contact forms having the same Webster scalar curvature.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences de Sfax, Route de Soukra, Sfax, Tunisia

    Hichem Chtioui

  2. Mathematisches Institut der Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany

    Mohameden Ould Ahmedou

  3. Institut Préparatoire aux Etudes d’Ingénieur de Monastir, Avenue Ibn Al Jazzar, 5019, Monastir, Tunisia

    Ridha Yacoub

Authors
  1. Hichem Chtioui
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  2. Mohameden Ould Ahmedou
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  3. Ridha Yacoub
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Correspondence to Mohameden Ould Ahmedou.

Additional information

Communicated by Yakov Eliashberg.

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Chtioui, H., Ahmedou, M.O. & Yacoub, R. Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds. J Geom Anal 23, 878–894 (2013). https://doi.org/10.1007/s12220-011-9267-z

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  • DOI: https://doi.org/10.1007/s12220-011-9267-z

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