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.
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收藏
页码：101 / 127
页数：27
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