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RIGIDITY CHARACTERIZATIONS OF COMPLETE RIEMANNIAN MANIFOLDS WITH α-BACH-FLAT

Guangyue Huang|Qianyu Zeng
대한수학회 (The Korean Mathematical Society)|2021.03|대한수학회지 (Journal of the KMS)|제58권 제2호|pp. 401-418|DOI 10.4134/JKMS.j200086

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참고문헌

키워드

EinsteinrigiditySobolev constantα-Bach-flat
주제분류수학

초록

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.

Abstract

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.

참고문헌 (19)

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