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# Mathematical Research Letters

## Volume 21 (2014)

### Number 2

### Some unstable critical metrics for the $L^{\frac{n}{2}}$-norm of the curvature tensor

Pages: 235 – 240

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n2.a2

#### Authors

#### Abstract

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold $M$ given by $\mathcal{R}_{\frac{n}{2}}(g):= \int_M |R(g)|^{\frac{n}{2}}dv_g$ where $R(g)$, $dv_g$ denote the Riemannian curvature and volume form corresponding to $g$. We show that there are locally symmetric spaces which are unstable critical points for this functional.

#### Keywords

Riemannian functional, stability

Published 1 August 2014