Morse index bounds for minimal submanifolds

Adauto, Diego ^[1] ; Batista, Márcio ^[2]
1. [1] Universidade do Estado do Rio Grande do Norte
  
  Universidade do Estado do Rio Grande do Norte
  
  Brasil
2. [2] Universidade Federal de Alagoas
  
  Universidade Federal de Alagoas
  
  Brasil
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 101-127
Idioma: inglés
DOI: 10.1007/s13348-022-00380-7
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Resumen
- 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.