Index of compact minimal submanifolds of the Berger spheres

The stability and the index of compact minimal submanifolds of the Berger spheres s(tau)(2n+1), 0 < tau <= 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(2) <= 1/2. Moreover, there are no stable compact minimal d-dimensional submanifolds of s(tau)(2n+1) when 1/(d+ 1) < tau(2) <= 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 with index one are classified for 1/3 <= tau(2) <= 1.