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In this paper, we study the critical metrics for quadratic curvature functionals involving the Ricci curvature and scalar curvature in the space of Riemannian metrics with unit volume. For these… Click to show full abstract
In this paper, we study the critical metrics for quadratic curvature functionals involving the Ricci curvature and scalar curvature in the space of Riemannian metrics with unit volume. For these functionals, Einstein metrics are always critical metrics. However, a converse problem is not always true. The purpose of this paper is to show that, under the condition that the critical metrics are Bach-flat, a partial converse is true.
Keywords:
metrics quadratic;
curvature functionals;
critical metrics;
quadratic curvature;
bach flat;
curvature
Journal Title: Annals of Global Analysis and Geometry
Year Published: 2018
Link to full text (if available)
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Journal Title: Annals of Global Analysis and Geometry
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!