Adviser: Peter B. Gilkey.
ix, 128 leaves / A print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000 / Relative to a non-degenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skew-symmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant dimension on the Grassmanian of non-degenerate oriented 2-planes. A pseudo-Riemannian manifold with a non-degenerate indefinite metric of signature (p, q) is said to be IP if the curvature tensor of the Levi-Civita connection is IP at every point; the eigenvalues are permitted to vary with the point. In the Riemannian setting (p, q) = (0, m), the work of Gilkey, Leahy, and Sadofsky and the work of Ivanov and Petrova have classified the IP metrics and IP algebraic curvature tensors if the dimension is at least 4 and if the dimension is not 7. We use techniques from algebraic topology and from differential geometry to extend some of their results to the Lorentzian setting (p, q) = (1, m – 1) and to the setting of metrics of signature (p, q) = (2, m – 2).
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/150 |
| Date | January 2000 |
| Creators | Zhang, Tan, 1969- |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | 5667358 bytes, 1473 bytes, 177540 bytes, application/pdf, text/plain, text/plain |
| Relation | University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 |
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