Diego Adauto, Márcio G. Batista Dias
In this paper, we study the Morse index of closed minimal submanifolds immersed into general Riemannian manifolds. Using the strategy developed by Ambrozio et al. (J Differ Geom 108(3):379–410, 2018) and under a suitable constrain on the submanifold, we obtain that the Morse index of the submanifold is bounded from below by a linear function of its first Betti’s number, as conjectured by Schoen and Marques-Neves. We also present many Riemannian manifolds and a sufficient condition to get the cited linear lower bound.
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