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The Geometry of Walker Manifolds
TLDR
In this Chapter, we introduce the algebraic structures that we will be using; the reader may want to read the next Chapter (which deals with the corresponding geometric structures) before reading this Chapter. Expand
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Osserman Manifolds in Semi-Riemannian Geometry
The Osserman Conditions in Semi-Riemannian Geometry.- The Osserman Conjecture in Riemannian Geometry.- Lorentzian Osserman Manifolds.- Four-Dimensional Semi-Riemannian Osserman Manifolds with MetricExpand
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Four-dimensional Osserman metrics with nondiagonalizable Jacobi operators
A complete description of Osserman four-manifolds whose Jacobi operators have a nonzero double root of the minimal polynomial is given.
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Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
Abstract Correspondence between torsion-free connections with nilpotent skew-symmetric curvature operator and IP Riemann extensions is shown. Some consequences are derived in the study ofExpand
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Applications of Affine and Weyl Geometry
TLDR
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. Expand
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The geometry of modified Riemannian extensions
We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. WeExpand
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Affine Osserman connections and their Riemann extensions
Abstract Osserman property is studied for affine torsion-free connections with special attention to the 2-dimensional case. As an application, examples of nonsymmetric and even not locallyExpand
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Four-dimensional Osserman–Ivanov–Petrova metrics of neutral signature
Algebraic curvature tensors which are Osserman–IP in the (− − + +)-signature setting are completely determined. As a consequence, it is shown that a four-dimensional pointwise Osserman–IP manifold isExpand
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