Conformally flat manifolds and a pinching problem on the Ricci tensor
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- by Samuel I. Goldberg and Masafumi Okumura PDF
- Proc. Amer. Math. Soc. 58 (1976), 234-236 Request permission
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.References
- Samuel I. Goldberg, On conformally flat spaces with definite Ricci curvature. II, K\B{o}dai Math. Sem. Rep. 27 (1976), no. 4, 445–448. MR 445427
- Masafumi Okumura, Submanifolds and a pinching problem on the second fundamental tensors, Trans. Amer. Math. Soc. 178 (1973), 285–291. MR 317246, DOI 10.1090/S0002-9947-1973-0317246-1
Additional Information
- © Copyright 1976 American Mathematical Society
- 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