Browsing Mathematics Theses and Dissertations by Author "Zhang, Tan, 1969"
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Zhang, Tan, 1969 (University of Oregon, 2000)[more][less]Zhang, Tan, 1969 20080210T03:23:11Z 20080210T03:23:11Z 2000 0599845562 http://hdl.handle.net/1794/150 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 nondegenerate metric of signature (p, q), an algebraic curvature tensor is said to be IP if the associated skewsymmetric curvature operator R(π) has constant eigenvalues and if the kernel of R(π) has constant dimension on the Grassmanian of nondegenerate oriented 2planes. A pseudoRiemannian manifold with a nondegenerate indefinite metric of signature (p, q) is said to be IP if the curvature tensor of the LeviCivita 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). 5667358 bytes 1473 bytes 177540 bytes application/pdf text/plain text/plain en_US University of Oregon University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 Manifolds (Mathematics) Metric spaces Curvature Operator algebras Eigenvalues Manifolds with indefinite metrics whose skewsymmetric curvature operator has constant eigenvalues Thesis
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