• Soma Maity

      Articles written in Proceedings – Mathematical Sciences

    • On the Stability of the $L^p$-Norm of the Riemannian Curvature Tensor

      Soma Maity

      More Details Abstract Fulltext PDF

      We consider the Riemannian functional $\mathcal{R}_p(g)=\int_M|R(g)|^p dv_g$ defined on the space of Riemannian metrics with unit volume on a closed smooth manifold 𝑀 where $R(g)$ and $dv_g$ denote the corresponding Riemannian curvature tensor and volume form and $p\in (0,\infty)$. First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for $\mathcal{R}_p$ for certain values of 𝑝. Then we conclude that they are strict local minimizers for $\mathcal{R}_p$ for those values of 𝑝. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for $\mathcal{R}_p$ for certain values of 𝑝.

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