dc.contributor.author |
Zhang, Tan, 1969- |
en_US |
dc.date.accessioned |
2008-02-10T03:23:11Z |
|
dc.date.available |
2008-02-10T03:23:11Z |
|
dc.date.issued |
2000 |
en_US |
dc.identifier.isbn |
0-599-84556-2 |
en_US |
dc.identifier.uri |
http://hdl.handle.net/1794/150 |
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dc.description |
Adviser: Peter B. Gilkey.
ix, 128 leaves |
en_US |
dc.description |
A print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000 |
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dc.description.abstract |
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). |
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5667358 bytes |
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1473 bytes |
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177540 bytes |
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application/pdf |
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text/plain |
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text/plain |
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dc.language.iso |
en_US |
en_US |
dc.publisher |
University of Oregon |
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dc.relation.ispartofseries |
University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 |
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dc.subject |
Manifolds (Mathematics) |
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dc.subject |
Metric spaces |
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dc.subject |
Curvature |
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dc.subject |
Operator algebras |
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dc.subject |
Eigenvalues |
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dc.title |
Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues |
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dc.type |
Thesis |
en_US |