On Vanishing Theorems for Locally Conformally Flat Riemannian Manifolds with an Integral Pinching Condition

被引：0

作者：

Pham, Duc Thoan ^{[1
]}

Tran, Van Khien ^{[1
]}

Nguyen, Thi Hong ^{[2
]}

机构：

[1] Hanoi Univ Civil Engn, Dept Math, 55 Giai Phong Rd, Hanoi, Vietnam

[2] Acad Cryptog Tech, Dept Fdn, 141 Chien Thang Rd, Hanoi, Vietnam

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2023年

关键词：

Harmonic p-form; Vanishing theorem; Locally conformally flat Riemannian manifold; P-HARMONIC; 1-FORMS; WEIGHTED POINCARE INEQUALITY; FORMS; SUBMANIFOLDS; CURVATURE;

D O I：

10.1007/s40304-023-00372-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show some vanishing theorems for harmonic p-forms on a locally conformally flat Riemannian manifold. In the concrete, provided that the integral of the traceless Ricci tensor has a suitable bound, we obtain a vanishing theorem for them without any scalar curvature conditions. Another theorem is also given under the condition on nonpositive scalar curvature, which improves and extends the ones previous.

引用

页数：12

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