منابع مشابه
Conformally Osserman Manifolds
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...
متن کاملOsserman manifolds of dimension 8
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.
متن کاملHigher Order Jordan Osserman Pseudo-riemannian Manifolds
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and nontrivial examples of higher order Osserman manifolds. Subject Classification: 53B20. PACS numbers: 0240, 0...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2010
ISSN: 0030-8730
DOI: 10.2140/pjm.2010.245.315