Index of compact minimal submanifolds of the Berger spheres
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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]
SponsorshipProject PID2019.111531GA.I00 funded by MCIN/AEI/10.13039/501100011033; Programa Operativo FEDER Andalucía 2014-2020, grant no. E-FQM-309-UGR18; Regional J. Andalucía grant no. P18-FR-4049
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.