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dc.contributor.authorZhang, Tan, 1969-en_US
dc.date.accessioned2008-02-10T03:23:11Z
dc.date.available2008-02-10T03:23:11Z
dc.date.issued2000en_US
dc.identifier.isbn0-599-84556-2en_US
dc.identifier.urihttp://hdl.handle.net/1794/150en_US
dc.descriptionAdviser: Peter B. Gilkey. ix, 128 leavesen_US
dc.descriptionA print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000en_US
dc.description.abstractRelative 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).en_US
dc.format.extent5667358 bytes
dc.format.extent1473 bytes
dc.format.extent177540 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
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dc.language.isoen_USen_US
dc.publisherUniversity of Oregonen_US
dc.relation.ispartofseriesUniversity of Oregon theses, Dept. of Mathematics, Ph. D., 2000en_US
dc.subjectManifolds (Mathematics)en_US
dc.subjectMetric spacesen_US
dc.subjectCurvatureen_US
dc.subjectOperator algebrasen_US
dc.subjectEigenvaluesen_US
dc.titleManifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvaluesen_US
dc.typeThesisen_US


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