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, Volume 159, Issue 1–2, pp 183–202 | Cite as

On the stability of \(L^p\)-norms of Riemannian curvature at rank one symmetric spaces

  • Soma MaityEmail author
Article
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Abstract

We study stability and local minimizing property 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 \(p\ge 2\). A similar result also holds for compact quotients of rank 1 symmetric spaces of non-compact type. Consequently, we obtain stability of \(L^{\frac{n}{2}}\)-norm of Weyl curvature at these metrics using results from Gursky and Viaclovsky (J Reine Angew Math 400:37–91, 2015).

Mathematics Subject Classification

Primary 53C21 58E11 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research MohaliMohaliIndia

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