An Osserman-type condition on g.f.f-manifolds with Lorentz metric
نویسندگان
چکیده
منابع مشابه
Completeness, Ricci Blowup, the Osserman and the Conformal Osserman Condition for Walker Signature (2, 2) Manifolds
Walker manifolds of signature (2, 2) have been used by many authors to provide examples of Osserman and of conformal Osserman manifolds of signature (2, 2). We study questions of geodesic completeness and Ricci blowup in this context.
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An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension n 6= 3, 4, 16 is locally conformally equivalent either to a Euclidean space or to a...
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For a Riemannian manifold M n with the curvature tensor R, the Jacobi operator RX is defined by RX Y = R(X, Y)X. The manifold M n is called pointwise Osserman if, for every p ∈ M n , the eigenvalues of the Jacobi operator RX do not depend of a unit vector X ∈ TpM n , and is called globally Osserman if they do not depend of the point p either. R. Osserman conjectured that globally Osserman manif...
متن کامل, Osserman and Ivanov - Petrova Pseudo - Riemannian Manifolds
We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.
متن کاملSzabó Osserman Ip Pseudo-riemannian Manifolds
We construct a family of pseudo-Riemannian manifolds so that the skew-symmetric curvature operator, the Jacobi operator, and the Szabó operator have constant eigenvalues on their domains of definition. This provides new and non-trivial examples of Osserman, Szabó, and IP manifolds. We also study when the associated Jordan normal form of these operators is constant. Subject Classification: 53B20.
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2014
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap110-2-3