Index of compact minimal submanifolds of the Berger spheres Torralbo Torralbo, Francisco Urbano Pérez-Aranda, Francisco Differential geometry The stability and the index of compact minimal submanifolds of the Berger spheres S2n+1τ,0<τ≤1, are studied. Unlike the case of the standard sphere (τ=1), where there are no stable compact minimal submanifolds, the Berger spheres have stable ones if and only if τ2≤1/2. Moreover, there are no stable compact minimal d-dimensional submanifolds of S2n+1τ when 1/(d+1)<τ2≤1 and the stable ones are classified for τ2=1/(d+1) when the submanifold is embedded. Finally, the compact orientable minimal surfaces of S3τ with index one are classified for 1/3≤τ2≤1. 2022-04-22T07:37:33Z 2022-04-22T07:37:33Z 2022-03-02 info:eu-repo/semantics/article Published version: Torralbo, F., Urbano, F. Index of compact minimal submanifolds of the Berger spheres. Calc. Var. 61, 104 (2022). [https://doi.org/10.1007/s00526-022-02215-6] http://hdl.handle.net/10481/74448 10.1007/s00526-022-02215-6 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España