# 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} }

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

### Conformally Osserman manifolds

- Mathematics
- 2008

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…

### Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues

- MathematicsProceedings 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…

### Conformally Osserman manifolds of dimension 16 and a Weyl–Schouten theorem for rank-one symmetric spaces

- Mathematics
- 2012

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…

### Osserman manifolds and Weyl-Schouten Theorem for rank-one symmetric spaces

- Mathematics
- 2009

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…

### Osserman and Conformally Osserman Manifolds with Warped and Twisted Product Structure

- 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…

### CURVATURE STRUCTURE OF SELF-DUAL 4-MANIFOLDS

- 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…

### Weyl–Schouten Theorem for symmetric spaces

- Mathematics
- 2013

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…

### Conformally Osserman manifolds of dimension 16 and a Weyl–Schouten theorem for rank-one symmetric spaces

- MathematicsAnnali di Matematica Pura ed Applicata
- 2011

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…

### The Geometry of Walker Manifolds

- MathematicsThe Geometry of Walker Manifolds
- 2009

This paper discusses Walker Structures, Lorentzian Walker Manifolds, and the Spectral Geometry of the Curvature Tensor.

### A ug 2 00 7 STANILOV – TSANKOV – VIDEV THEORY

- 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

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- 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…

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- Mathematics
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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.

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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,…

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