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8-dimensional Einstein-Thorpe manifolds

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 April 2009

Jaeman Kim
Jaeman Kim
Affiliation:
Department of Mathematics Yonsei University Shinchon 134 Seoul Korea e-mail: jaeman@math.yonsei.ac.kr
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Abstract

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We prove that a compact orientable Einstein-Thorpe manifold of dimension 8 that satisfies 6X = |P2| must be flat.

Keywords

Einstein-Thorpe manifoldflat

MSC classification

Secondary: 53B20: Local Riemannian geometry 53B21: Methods of Riemannian geometry 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 2 , April 2000 , pp. 278 - 284
Copyright
Copyright © Australian Mathematical Society 2000

References

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[4]Kim, J. M., Einstein-Thorpe manifolds (Ph. D. Thesis, S.U.N.Y at Stony Brook, 1998).Google Scholar
[5]Thorpe, J. A., ‘Some remarks on the Gauss-Bonnet integral’, J. Math. Mech. 18 (1969), 779–786.Google Scholar