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

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Title: Manifolds with indefinite metrics whose skew-symmetric curvature operator has constant eigenvalues
Author: Zhang, Tan, 1969-
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).
Description: Adviser: Peter B. Gilkey. ix, 128 leavesA print copy of this title is available through the UO Libraries under the call number: MATH QA613 .Z43 2000
URI: http://hdl.handle.net/1794/150
Date: 2000


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