• Corpus ID: 118859396

Conformally Osserman manifolds and self-duality in Riemannian geometry

```@article{Blai2005ConformallyOM,
title={Conformally Osserman manifolds and self-duality in Riemannian geometry},
author={Novica Bla{\vz}i{\'c} and Peter Gilkey},
journal={arXiv: Differential Geometry},
year={2005}
}```
• Published 25 April 2005
• Mathematics
• arXiv: Differential Geometry
We study the spectral geometry of the conformal Jacobi operator on a 4-dimensional Riemannian manifold (M,g). We show that (M,g) is conformally Osserman if and only if (M,g) is self-dual or anti self-dual. Equivalently, this means that the curvature tensor of (M,g) is given by a quaternionic structure, at least pointwise.
• 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
• 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
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
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
• Mathematics
• 2013
Abstract. Let be a 4-dimensional almost-Hermitian manifold which satisfies the Kähler identity. We show that is complex Osserman if and only if has constant holomorphic sectional curvature. We also
• Mathematics
• 2010
Let H be a 4 dimensional almost Hermitian manifold which satisfies the Kaehler identity. Then H is complex Osserman if and only if H has constant holomorphic sectional curvature. We also classify in
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

References

SHOWING 1-9 OF 9 REFERENCES

• Mathematics
• 2004
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
• 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
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
Osserman conjectured that if the curvature operatorR of a Riemannian manifoldM has constant eigenvalues, thenM is locally a rank-1 symmetric space or is flat. The pointwise question is considerably
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,
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