An obstruction for the mean curvature of a conformal immersion Sn-> Rn+1
by
Bernd Ammann, Emmanuel Humbert, Mohameden Ould Ahmedou


An obstruction for the mean curvature of a conformal immersion Sn-> Rn+1 (.dvi, .ps,.ps.gz or .pdf)
Proc.~AMS. 135 489-493 (2007)

Abstract

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 Sn-> Rn+1 satisfies $\int \partial_X H=0$ where X is a conformal vector field on Sn 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 Sn inside the standard conformal class.
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The Paper was written on 28.6.2005
Last update 28.6.2005