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Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators
E. Calvino-Louzao, E. Garcia-Rio, P. Gilkey +1
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 adm…
Compact Osserman manifolds with neutral metric
M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey +1
It is shown that if a compact four-dimensional manifold with metric of neutral signature is Jordan-Osserman, then it is either of constant sectional curvature or Ricci flat.
Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds
M. Brozos-Vazquez, P. Gilkey, E. Garcia-Rio +1
Walker manifolds of signature (2,2) have been used to provide examples of Osserman and of conformal Osserman manifolds of signature (2,2). We study questions of geodesic completene…