Conformally flat manifolds with nonnegative Ricci curvature
نویسندگان
چکیده
منابع مشابه
Conformally Flat Manifolds with Nonnegative Ricci Curvature
We show that complete conformally flat manifolds of dimension n > 3 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to R n or a spherical spaceform Sn/Γ. This extends previous results due to Q.-M. Cheng and B.-L. Chen and X.-P. Zhu. In this note, we study compl...
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Abstract. We study the equation ∆gu− n−2 4(n−1)R(g)u+Ku p = 0 (1+ ζ ≤ p ≤ n+2 n−2 ) on locally conformally flat compact manifolds (M, g). We prove the following: (i) When the scalar curvature R(g) > 0 and the dimension n ≥ 4, under suitable conditions on K, all positive solutions u have uniform upper and lower bounds; (ii) When the scalar curvature R(g) ≡ 0 and n ≥ 5, under suitable conditions ...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2006
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x06002016