Rigidity theorem for compact Bach-flat manifolds with positive constant ${\sigma }_2$

Abstract

We prove that an n($\ge$ 4)-dimensional compact Bach-flat manifold with positive constant ${\sigma }_2$ is an Einstein manifold, provided that its Weyl curvature satisfies a suitable pinching condition.

arXiv commentarXiv admin note: text overlap with arXiv:1707.07236

References in corpus (2)

• Fourth order curvature flows and geometric applications
• Rigidity of noncompact complete Bach-flat manifolds