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

Josef Mikeš, Vladimir Rovenski, Sergey Stepanov and Irina Tsyganok
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Josef Mikeš: Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic
Vladimir Rovenski: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 3498838, Israel
Sergey Stepanov: Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia
Irina Tsyganok: Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia

Mathematics, 2021, vol. 9, issue 9, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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