Variational properties of quadratic curvature functionals

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（9）
• 页码范围: 1765-1778
• 页数: 14页
• 语种: 英文

摘要

In this paper,we investigate a class of quadratic Riemannian curvature functionals on closed smooth manifold M of dimension n ≥ 3 on the space of Riemannian metrics on M consisting of metrics with unit volume.We study the stability of these functionals at the metric with constant sectional curvature as its critical point.