Morse index bounds for minimal submanifolds

被引：1

作者：

Adauto, Diego ^{[1
]}

Batista, Marcio ^{[2
]}

机构：

[1] Univ Estado Rio Grande do Norte, DME, BR-59610210 Mossoro, RN, Brazil

[2] Univ Fed Alagoas, CPMAT IM, BR-57072970 Maceio, Alagoas, Brazil

来源：

COLLECTANEA MATHEMATICA | 2024年 / 75卷 / 01期

关键词：

Submanifolds; Morse index; Betti number; High codimension; HYPERSURFACES; SURFACES; REAL;

D O I：

10.1007/s13348-022-00380-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：101 / 127

页数：27

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