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arXiv · 0906.0475

Existence and Multiplicity results for the prescribed Webster Scalar Curvature Problem on three $C R $ manifolds

H. Chtioui·M. Ould Ahmedou·R. Yacoub
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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 $\mathbb{C}^{2}$. 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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H. Chtioui, M. Ould Ahmedou, R. Yacoub. 2009-06-02. Existence and Multiplicity results for the prescribed Webster Scalar Curvature Problem on three $C R $ manifolds. https://arxiv.org/abs/0906.0475

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