Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature

被引：5

作者：

Lin, Hezi ^{[1
,2
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350108, Fujian, Peoples R China

[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350108, Fujian, Peoples R China

来源：

GEOMETRIAE DEDICATA | 2019年 / 201卷 / 01期

关键词：

Harmonic forms; Vanishing theorems; Betti numbers; Weighted Poincare inequalities; WEIGHTED POINCARE INEQUALITY; HARMONIC FORMS;

D O I：

10.1007/s10711-018-0388-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show several vanishing theorems for harmonic p-forms on compact manifolds, and Lq harmonic p-forms on complete noncompact manifolds with nonnegative scalar curvature, under various pointwise or integral curvature conditions. These conditions involve the positive Yamabe invariant, the weighted Poincare inequality and the pure curvature tensor.

引用

页码：187 / 201

页数：15

共 50 条

[1] Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature
Hezi Lin
[J]. Geometriae Dedicata, 2019, 201 : 187 - 201
[2] Vanishing Theorems for Riemannian Manifolds with Nonnegative Scalar Curvature and Weighted p-Poincare Inequality
Pham, Duc Thoan
Nguyen, Dang Tuyen
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (06) : 3541 - 3551
[3] Vanishing Theorems for Riemannian Manifolds with Nonnegative Scalar Curvature and Weighted p-Poincaré Inequality
Duc Thoan Pham
Dang Tuyen Nguyen
[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 3541 - 3551
[4] SPLITTING THEOREMS ON COMPLETE RIEMANNIAN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE
Farina, Alberto
Ocariz, Jesus
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (04) : 1929 - 1937
[5] L2 CURVATURE PINCHING THEOREMS AND VANISHING THEOREMS ON COMPLETE RIEMANNIAN MANIFOLDS
Dong, Yuxin
Lin, Hezi
Wei, Shihshu Walter
[J]. TOHOKU MATHEMATICAL JOURNAL, 2019, 71 (04) : 581 - 607
[6] Scalar curvature on noncompact complete Riemannian manifolds
Kim, ST
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (12) : 1985 - 1993
[7] RIGIDITY RESULTS FOR COMPLETE MANIFOLDS WITH NONNEGATIVE SCALAR CURVATURE
Zhu, Jintian
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 2023, 125 (03) : 623 - 644
[8] Problems of the prescribed scalar curvature on complete Riemannian manifolds
Aubin, T
Cotsiolis, A
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2002, 81 (10): : 999 - 1009
[9] FINITENESS AND VANISHING THEOREMS FOR COMPLETE OPEN RIEMANNIAN-MANIFOLDS
SHEN, ZM
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 21 (02) : 241 - 244
[10] GENERALIZED SCALAR CURVATURE TYPE EQUATION ON COMPLETE RIEMANNIAN MANIFOLDS
Benalili, Mohammed
Maliki, Youssef
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2004,

← 1 2 3 4 5 →