Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds

Abstract

In this article, we discuss the global aspects of the geometry of locally conformally flat (complete and compact) Riemannian manifolds. In particular, the article reviews and improves some results (e.g., the conditions of compactness and degeneration into spherical or flat space forms) on the geometry “in the large" of locally conformally flat Riemannian manifolds. The results presented here were obtained using the generalized and classical Bochner technique, as well as the Ricci flow.

Keywords

• Riemannian manifold
• locally conformally flat
• curvature operator
• scalar and Ricci curvatures
• Ricci flow