Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues

Show simple item record Zhang, Tan, 1969- en_US 2008-02-10T03:23:11Z 2008-02-10T03:23:11Z 2000 en_US
dc.identifier.isbn 0-599-84556-2 en_US
dc.identifier.uri en_US
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 en_US
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). en_US
dc.format.extent 5667358 bytes
dc.format.extent 1473 bytes
dc.format.extent 177540 bytes
dc.format.mimetype application/pdf
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dc.language.iso en_US en_US
dc.publisher University of Oregon en_US
dc.relation.ispartofseries University of Oregon theses, Dept. of Mathematics, Ph. D., 2000 en_US
dc.subject Manifolds (Mathematics) en_US
dc.subject Metric spaces en_US
dc.subject Curvature en_US
dc.subject Operator algebras en_US
dc.subject Eigenvalues en_US
dc.title Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues en_US
dc.type Thesis en_US

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