Compact Osserman manifolds with neutral metric
M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, and R. Vazquez-Lorenzo
TL;DR
This paper proves that compact four-dimensional neutral signature manifolds that are Jordan-Osserman must be either of constant sectional curvature or Ricci flat, providing a classification under these conditions.
Contribution
It establishes a classification result for compact four-dimensional Jordan-Osserman manifolds with neutral metrics, identifying their geometric types.
Findings
Such manifolds are either of constant sectional curvature or Ricci flat.
The result narrows the possible geometries of Jordan-Osserman manifolds in this setting.
Abstract
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology