Volume comparison theorem with respect to sigma-2 curvature

Abstract

In this paper, we investigate the volume comparison theorem related to ${\sigma }_2$-curvature. In particular, we show that volume comparison theorem with respect to ${\sigma }_2$-curvature holds for metrics close to strictly stable positive Einstein metrics. By applying similar techniques, we derive the local rigidity theorem for strictly stable Ricci flat manifolds with respect to ${\sigma }_2$-curvature, which shows it admits no metric with positive ${\sigma }_2$-curvature near strictly stable Ricci-flat metrics.

18 pages

References in corpus (1)

• Deformations of Q-curvature II