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COMPACT LOCALLY CONFORMALLY FLAT RIEMANNIAN MANIFOLDS

Published online by Cambridge University Press:  25 July 2001

QING-MING CHENG
QING-MING CHENG
Affiliation:
Department of Mathematics, Faculty of Science, Josai University, Saitama, Sakado 350-0295, Japan; cheng@math.josai.ac.jp
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Abstract

First, we shall prove that a compact connected oriented locally conformally flat n-dimensional Riemannian manifold with constant scalar curvature is isometric to a space form or a Riemannian product Sn−1(c) × S1 if its Ricci curvature is nonnegative. Second, we shall give a topological classification of compact connected oriented locally conformally flat n-dimensional Riemannian manifolds with nonnegative scalar curvature r if the following inequality is satisfied: [sum ]i,jR2ij [les ] r2/(n−1), where [sum ]i,jR2ij is the squared norm of the Ricci curvature tensor.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 459 - 465
Copyright
© The London Mathematical Society 2001

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