Rigidity of Einstein metrics as critical points of quadratic curvature functionals on closed manifolds. (October 2018)

• Record Type: Journal Article
• Authors: Ma, Bingqing; Huang, Guangyue; Li, Xingxiao; Chen, Yu
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 237
• Page End: 248
• Publication Date: 2018-10
• Subjects: primary 51H25 -- secondary 53C21; Critical metric -- Yamabe invariant -- Einstein -- Rigidity; 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.2018.05.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove some rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals on closed manifolds, characterized by some point-wise inequalities. Moreover, we also provide a few rigidity results that involve the Weyl curvature, the trace-less Ricci curvature and the Yamabe invariant, accordingly.