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Complete curvature homogeneous pseudo-Riemannian manifolds

Complete \(k\)-curvature homogeneous pseudo-Riemannian manifolds

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 15 Jul 2004Embargo end date: 01 Jan 2004Publisher:IOP PublishingJournal:Classical and Quantum Gravity, volume 21, pages 3,755-3,770 (issn: 0264-9381, eissn: 1361-6382,

Authors: Peter B. Gilkey; Stana Nikcevic;

doi: 10.1088/0264-9381/21/15/009 , 10.1007/s10455-005-5217-y , 10.48550/arxiv.math/0402282 , 10.48550/arxiv.math/0405024

arXiv: http://arxiv.org/abs/math/0405024 , http://arxiv.org/abs/math/0402282

Complete curvature homogeneous pseudo-Riemannian manifolds

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Abstract

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.

Update paper to fix misprints in original version

Related Organizations

University of Oregon
United States

Keywords

Mathematics - Differential Geometry, locally homogeneous, homogeneous spaces, FOS: Physical sciences, 53B20, Mathematical Physics (math-ph), pseudo-Riemannian manifolds, Jacobi operator, Jordan Ivanov-Petrova manifolds, affine k-curvature homogeneous manifold, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Local Riemannian geometry, Differential geometry of homogeneous manifolds, Differential Geometry (math.DG), completeness, Jordan Osserman manifolds, nilpotent, FOS: Mathematics, Linear and affine connections, Mathematical Physics

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