Homology Vanishing Theorems for Pinched Submanifolds

被引：1

作者：

Onti, Christos-Raent ^{[1
]}

Vlachos, Theodoros ^{[2
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

[2] Univ Ioannina, Dept Math, GR-45110 Ioannina, Greece

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2022年 / 32卷 / 12期

关键词：

Bochner operator; Betti numbers; Homology groups; Pinching; Mean curvature; Length of the second fundamental form; PARALLEL MEAN-CURVATURE; MINIMAL SUBMANIFOLDS; RICCI CURVATURE; SPHERE THEOREM; RIGIDITY THEOREMS; SPACE-FORMS; HYPERSURFACES; IMMERSIONS;

D O I：

10.1007/s12220-022-01032-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like the mean curvature and the length of the second fundamental form. Homology vanishing results are given that strengthen and sharpen previous ones. In addition, an integral bound is provided for the Bochner operator of compact Euclidean submanifolds in terms of the Betti numbers.

引用

页数：33

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