TL;DR
This paper investigates infinitesimal Einstein deformations on compact flat and product manifolds, providing refined obstructions to their existence under specific curvature conditions.
Contribution
It offers new insights and refinements to existing results by Koiso and Bourguignon regarding obstructions to Einstein deformations.
Findings
Identified conditions under which infinitesimal Einstein deformations cannot exist.
Provided refined obstructions based on curvature conditions.
Extended analysis to product manifolds and flat geometries.
Abstract
We study infinitesimal Einstein deformations on compact flat manifolds and on product manifolds. Moreover, we prove refinements of results by Koiso and Bourguignon which yield obstructions on the existence of infinitesimal Einstein deformations under certain curvature conditions.
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