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Conformally flat manifolds and a pinching problem on the Ricci tensor


Authors: Samuel I. Goldberg and Masafumi Okumura
Journal: Proc. Amer. Math. Soc. 58 (1976), 234-236
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1976-0410601-9
MathSciNet review: 0410601
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Abstract: There is a formal similarity between the theory of hypersurfaces and conformally flat $ d$-dimensional spaces of constant scalar curvature provided $ d \geq 3$. For, then, the symmetric linear transformation field $ Q$ defined by the Ricci tensor satisfies Codazzi's equation $ ({\nabla _X}Q)Y = ({\nabla _Y}Q)X$. This observation leads to a pinching theorem on the length of the Ricci tensor.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0410601-9
Keywords: Conformally flat manifolds, Ricci tensor, scalar curvature
Article copyright: © Copyright 1976 American Mathematical Society

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