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

Authors

Atreyee Bhattacharya (Department of Mathematics, Indian Institute of Science, Bangalore, India)

Soma Maity (Department of Mathematics, Indian Institute of Science, Bangalore, India)

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

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Published 1 August 2014