The nonexistence of rank 4 IP tensors in signature .
Pearson, Kelly Jeanne, Zhang, Tan (2002)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “Complex IP pseudo-Riemannian algebraic curvature tensors”
The nonexistence of rank 4 IP tensors in signature .
The Jordan normal form of higher order Osserman algebraic curvature tensors
Peter Gilkey, Raina Ivanova (2002)
Commentationes Mathematicae Universitatis Carolinae
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We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type in a vector space of signature . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
Nilpotent spacelike Jordan Osserman pseudo-Riemannian manifolds
Gilkey, P., Nikčević, S.
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Relating algebraic properties of the curvature tensor to geometry.
Gilkey, Peter B. (1999)
Novi Sad Journal of Mathematics
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The Riemannian curvature tensor and differentiable spaces
Adam Kowalczyk (1984)
Banach Center Publications
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A functional expression for the curvature of hyper-dimensional Riemannian spaces.
Sarić, Branko (2000)
Lobachevskii Journal of Mathematics
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Curvature tensors in dimension four which do not belong to any curvature homogeneous space
Oldřich Kowalski, Friedbert Prüfer (1994)
Archivum Mathematicum
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A six-parameter family is constructed of (algebraic) Riemannian curvature tensors in dimension four which do not belong to any curvature homogeneous space. Also a general method is given for a possible extension of this result.
On certain curvature conditions on Riemannian manifolds
Ryszard Deszcz, Wiesław Grycak (1990)
Colloquium Mathematicae
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Extended Derdziński-Shen theorem for curvature tensors
Carlo Alberto Mantica, Luca Guido Molinari (2012)
Colloquium Mathematicae
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We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.