Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds
M. Brozos-Vazquez, P. Gilkey, E. Garcia-Rio, and R. Vazquez-Lorenzo
TL;DR
This paper investigates geodesic completeness and Ricci blowup phenomena in Walker manifolds of signature (2,2), which serve as examples for Osserman and conformal Osserman manifolds, enhancing understanding of their geometric properties.
Contribution
It explores the conditions under which Walker (2,2) manifolds are complete or exhibit Ricci blowup, providing new insights into their geometric and curvature characteristics.
Findings
Identification of conditions for geodesic completeness
Characterization of Ricci blowup scenarios
Examples of Osserman and conformal Osserman manifolds
Abstract
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 completeness and Ricci blowup in this context.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology