Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T23:15:48.936Z Has data issue: false hasContentIssue false
  • English
  • Français

8-dimensional Einstein-Thorpe manifolds

Part of: Local differential geometry Global 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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Besse, A., Einstein manifolds (Springer, Berlin, 1986).Google Scholar
[2]Chern, S. S., ‘A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds’, Ann. of Math. 45 (1994), 747–752.CrossRefGoogle Scholar
[3]Hitchin, N. J., ‘Compact four-dimensional Einstein manifolds’, J. Differential Geom. 9 (1974), 435–444.CrossRefGoogle Scholar
[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