# CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS

```@article{Blai2003CONFORMALLYOM,
title={CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS},
author={Novica Bla{\vz}i{\'c} and Peter Gilkey},
journal={International Journal of Geometric Methods in Modern Physics},
year={2003},
volume={01},
pages={97-106}
}```
• Published 16 November 2003
• Mathematics
• International Journal of Geometric Methods in Modern Physics
We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Jacobi operator associated to the Weyl conformal curvature tensor of a Riemannian manifold has constant eigenvalues on the bundle of unit tangent vectors and classify such manifolds…
16 Citations
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
• Mathematics
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2006
Conformal Osserman four-dimensional manifolds are studied with special attention to the construction of new examples showing that the algebraic structure of any such curvature tensor can be realized
A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are constant on the unit
A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are constant on the unit
• Mathematics
• 2008
Abstract.We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and
• Mathematics
• 2008
We show the existence of a modified Cliff(1,1)-structure compatible with an Osserman 0-model of signature (2,2). We then apply this algebraic result to certain classes of pseudo-Riemannian manifolds
Let M0 be a symmetric space of dimension n > 5 whose de Rham decomposition contains no factors of constant curvature and let W0 be the Weyl tensor of M0 at some point. We prove that a Riemannian
A Riemannian manifold is called Osserman (conformally Osserman, respectively), if the eigenvalues of the Jacobi operator of its curvature tensor (Weyl tensor, respectively) are constant on the unit
• Mathematics
The Geometry of Walker Manifolds
• 2009
This paper discusses Walker Structures, Lorentzian Walker Manifolds, and the Spectral Geometry of the Curvature Tensor.
• Mathematics
We shall discuss some recent results concerning Stanilov–Tsankov– Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the

## References

SHOWING 1-10 OF 13 REFERENCES

• Mathematics
• 2003
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in
• Mathematics
• 2002
The Osserman Conditions in Semi-Riemannian Geometry.- The Osserman Conjecture in Riemannian Geometry.- Lorentzian Osserman Manifolds.- Four-Dimensional Semi-Riemannian Osserman Manifolds with Metric
Abstract.Let Mn be a Riemannian manifold and R its curvature tensor. For a point p ∈ Mn and a unit vector X ∈ TpMn, the Jacobi operator is defined by RX=R(X,·)X. The manifold Mn is called pointwise
It is shown by means of Young symmetrizers and a theorem of S. Cummins that every algebraic curvature Tensor has a structure which is very similar to that of the above Osserman curvature tensors.
ROBERT OSSERMAN wrote a Ph.D. thesis on Riemann surfaces under the direction of Lars V. Ahlfors at Harvard University. He gradually moved from geometric function theory to minimal surfaces,
Algebraic curvature tensors the skew-symmetric curvature operator the Jacobi operator controlling the eigenvalue structure.