Article

# Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators

• ##### Ramón Vázquez-Lorenzo
Geometriae Dedicata (Impact Factor: 0.47). 07/2010; DOI: 10.1007/s10711-011-9595-y
Source: arXiv

ABSTRACT We exhibit Osserman metrics with non-nilpotent Jacobi operators and with non-trivial Jordan normal form in neutral signature (n,n) for any n which is at least 3. These examples admit a natural almost para-Hermitian structure and are semi para-complex Osserman with non-trivial Jordan normal form as well; they neither satisfy the third Gray identity nor are they integrable.

0 Bookmarks
·
80 Views
• Source
##### Article: THE RIEMANN EXTENSION OF AN AFFINE OSSERMAN CONNECTION ON 3-DIMENSIONAL MANIFOLD
[Hide abstract]
ABSTRACT: The Riemannian extension of torsion free affine manifolds ( M, ∇) is an important method to produce pseudo-Riemannian manifolds. It is know that, if the manifold ( M, ∇) is a torsion-free affine two-dimensional manifold with skew symmetric tensor Ricci, then ( M, ∇) is affine Osserman manifold. In higher dimensions the skew symmetric of the tensor Ricci is a necessary but not sufficient condition for a affine connection to be Osserman. In this paper we construct affine Osserman connection with Ricci flat but not flat and example of Osserman pseudo-Riemannian metric of signature (3, 3) is exhibited.
Global Journal of Advanced Research on Classical and Modern Geometries. 10/2013; 2(2):69-75.
• Source
##### Article: Two families of affine Osserman connections on3-dimensional manifolds
[Hide abstract]
ABSTRACT: The aim of this note is to study the Osserman condition on two families affine connections. As applications, examples of affine Osserman connections which are Ricci flat but not flat are given.
African Diaspora Journal of Mathematics. 02/2013; 14(2):178–186.