On the structure of conformally flat Riemannian manifolds. (August 2015)

• Record Type: Journal Article
• Authors: Lin, Hezi
• Is Part Of: Nonlinear analysis. Volume 123/124(2015)
• Page Start: 115
• Page End: 125
• Publication Date: 2015-08
• Subjects: 53C20 -- 53C25; Conformally flat -- L2-harmonic 1-forms -- Vanishing theorems -- Ends; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.001
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we will prove vanishing and finiteness theorems for L 2 -harmonic 1-forms on a locally conformally flat Riemannian manifold which satisfies an integral pinching condition on the traceless Ricci tensor, and for which the scalar curvature is non-positive or satisfies some integral pinching conditions. Based on these vanishing and finiteness theorems, combining with the work of Li–Tam, we can obtain some one-end and finite ends theorems.