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- W3206802493 abstract "The stability and the index of compact minimal submanifolds of the Berger spheres $${mathbb {S}}^{2n+1}_{tau },, 0<tau le 1$$ , are studied. Unlike the case of the standard sphere ( $$tau =1$$ ), where there are no stable compact minimal submanifolds, the Berger spheres have stable ones if and only if $$tau ^2le 1/2$$ . Moreover, there are no stable compact minimal d-dimensional submanifolds of $${mathbb {S}}^{2n+1}_tau $$ when $$1 / (d+1) < tau ^2 le 1$$ and the stable ones are classified for $$tau ^2=1 / (d+1)$$ when the submanifold is embedded. Finally, the compact orientable minimal surfaces of $${mathbb {S}}^3_{tau }$$ with index one are classified for $$1/3le tau ^2le 1$$ ." @default.
- W3206802493 created "2021-10-25" @default.
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- W3206802493 date "2022-04-07" @default.
- W3206802493 modified "2023-10-18" @default.
- W3206802493 title "Index of compact minimal submanifolds of the Berger spheres" @default.
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- W3206802493 doi "https://doi.org/10.1007/s00526-022-02215-6" @default.
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