Extended Graph 4-Manifolds, and Einstein Metrics
Luca F. Di Cerbo
TL;DR
This paper proves that extended graph 4-manifolds, a class of 4-dimensional manifolds, cannot admit Einstein metrics, thus clarifying their geometric structure.
Contribution
It establishes a non-existence result for Einstein metrics on extended graph 4-manifolds, expanding understanding of their geometric properties.
Findings
Extended graph 4-manifolds do not support Einstein metrics.
Provides a classification constraint for these manifolds.
Clarifies the geometric limitations of this manifold class.
Abstract
We show that extended graph 4-manifolds (as defined by Frigerio-Lafont-Sisto in [FLS15]) do not support Einstein metrics.
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