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

共 50 条

[21] VECTOR-BUNDLES WITH SEMIDEFINITE CURVATURE AND CO-HOMOLOGY VANISHING THEOREMS
GIGANTE, G
ADVANCES IN MATHEMATICS, 1981, 41 (01) : 40 - 56
[22] KOSTANT FORMULA AND HOMOLOGY VANISHING THEOREMS FOR GENERALIZED KAC-MOODY ALGEBRAS
NAITO, S
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1993, 33 (03): : 709 - 722
[23] Vanishing homology
Valette, Guillaume
SELECTA MATHEMATICA-NEW SERIES, 2010, 16 (02): : 267 - 296
[24] Vanishing homology
Guillaume Valette
Selecta Mathematica, 2010, 16 : 267 - 296
[25] Mean curvature flow of pinched submanifolds of CPn
Pipoli, G.
Sinestrari, C.
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2017, 25 (04) : 799 - 846
[26] On Yau Rigidity Theorem for Submanifolds in Pinched Manifolds
Xu, Hong-Wei
Lei, Li
Gu, Juan-Ru
PURE AND APPLIED MATHEMATICS QUARTERLY, 2016, 12 (02) : 301 - 333
[27] MEAN CURVATURE FLOW OF PINCHED SUBMANIFOLDS TO SPHERES
Andrews, Ben
Baker, Charles
JOURNAL OF DIFFERENTIAL GEOMETRY, 2010, 85 (03) : 357 - 395
[28] Vanishing theorems
Iskovskikh V.A.
Journal of Mathematical Sciences, 2001, 106 (5) : 3258 - 3268
[29] Vanishing theorems
Fujino, Osamu
MINIMAL MODELS AND EXTREME RAYS (KYOTO, 2011), 2016, 70 : 299 - 321
[30] VANISHING THEOREMS
VIEHWEG, E
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1982, 335 : 1 - 8

← 1 2 3 4 5 →