On the stability of L^p-norms of Curvature Tensor at Rank one symmetrics spaces

Abstract

We study stability and local minimizing properties of $L^p$- norms of Riemannian curvature tensor denoted by ${\mathcal{R}}_p$ by variational methods. We compute the Hessian of ${\mathcal{R}}_p$ at compact rank 1 symmetric spaces and prove that they are stable for ${\mathcal{R}}_p$ for certain values of p > 2. A similar result also holds for compact quotients of rank 1 symmetric spaces of non-compact type. Consequently, we obtain stability of L^{n\2}- norm of Weyl curvature at these metrics.

arXiv comment15 Pages and 1 figure

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