A generalization of a 4-dimensional Einstein manifold |
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| Authors: | Yunhee Euh Jeong Hyeong Park Kouei Sekigawa |
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| Affiliation: | 1121. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea
2121. Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
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| Abstract: | A weakly Einstein manifold is a natural generalization of a 4-dimensional Einstein manifold. In this paper, we shall give a characterization of a weakly Einstein manifold in terms of so-called generalized Singer-Thorpe bases. As an application, we prove a generalization of the Hitchin inequality for compact weakly Einstein 4-manifolds. Examples are provided to illustrate the theorems. |
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