Abstract
We show that on an 8-dimensional manifold with Euler characteristic zero every semiflat metric must be flat.
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References
Chern S. S., “A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds,” Ann. Math., 45, 747–752 (1944).
Thorpe J. A., “Some remarks on the Gauss-Bonnet integral,” J. Math. Mech., 18, 779–786 (1969).
Besse A. L., Einstein Manifolds, Springer-Verlag, Berlin (1986).
Kim J. Einstein-Thorpe manifolds, PhD Thesis in S.U.N.Y at stony brook (1998).
Kuiper H. N., “On conformally flat spaces in the large,” Ann. Math., 50, 916–924 (1949).
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Kim, H., Kim, J. An Equivalent Flat Condition. Siberian Mathematical Journal 44, 817–820 (2003). https://doi.org/10.1023/A:1025984703023
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DOI: https://doi.org/10.1023/A:1025984703023