The duality principle for Osserman algebraic curvature tensors

  title={The duality principle for Osserman algebraic curvature tensors},
  author={Y.Nikolayevsky and Z. Raki'c},
  journal={Linear Algebra and its Applications},

On quasi-Clifford Osserman curvature tensors

We consider pseudo-Riemannian generalizations of Osserman, Clifford, and the duality principle properties for algebraic curvature tensors and investigate relations between them. We introduce quasi-

On the existence of a curvature tensor for given Jacobi operators

The main theorem is generalized to the proportionality principle for Osserman algebraic curvature tensors and to the case of indefinite scalar product space.

On Lorentzian spaces of constant sectional curvature

We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant

The Proportionality Principle for Osserman Manifolds

Two-root Riemannian Manifolds

Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce $k$-root manifolds in which the reduced Jacobi operator has exactly $k$ eigenvalues. We investigate



On duality principle in Osserman manifolds

A note on Raki\'c duality principle for Osserman manifolds

In this note we prove that for a Riemannian manifold the Osserman pointwise condition is equivalent to the Raki\'c duality principle.

Duality principle and special Osserman manifolds

We investigate the connection between the duality principle and the Osserman condition in a pseudo-Riemannian setting. We prove that a connected pointwise two-leaves Osserman manifold of

On some aspects of duality principle

This paper is devoted to the study of the relation between Osserman algebraic curvature tensors and algebraic curvature tensors which satisfy the duality principle. We give a short overview of the

Spacelike Jordan Osserman algebraic curvature tensors in the higher signature setting

Let $R$ be an algebraic curvature tensor on a vector space of signature $(p,q)$ defining a spacelike Jordan Osserman Jacobi operator $\JJ_R$. We show that the eigenvalues of $\JJ_R$ are real and that

The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds

The Geometry of the Riemann Curvature Tensor Curvature Homogeneous Generalized Plane Wave Manifolds Other Pseudo-Riemannian Manifolds The Curvature Tensor Complex Osserman Algebraic Curvature Tensors

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 Metric

Osserman manifolds of dimension 8

Abstract.For a Riemannian manifold Mn with the curvature tensor R, the Jacobi operator RX is defined by RXY=R(X,Y)X. The manifold Mn is called pointwise Osserman if, for every p ∈ Mn, the eigenvalues


For a Riemannian manifold Mn with the curvature tensor R, the Jacobi operator RX is defined by RXY = R(X, Y )X. The manifold M n is called pointwise Osserman if, for every p ∈ Mn, the eigenvalues of