A Pohozaev type identity for Dirac operators
Résumé
We prove a Pohozaev type identity for non-linear eigenvalue equations of the Dirac operator on Riemannian spin manifolds with boundary. As an application, we obtain that the mean curvature $H$ of a conformal immersion $S^n\to \mR^{n+1}$ satisfies $\int \pa_X H=0$ where $X$ is a conformal vector field on $S^n$ and where the integration is carried out with respect to the Euclidean volume measure of the image. This identity is analogous to the Kazdan-Warner obstruction that appears in the problem of prescribing the scalar curvature on $S^n$ inside the standard conformal class.
Domaines
Géométrie différentielle [math.DG]
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