Remarks on $η$-Einstein unit tangent bundles

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135862We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $η$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is $η$-Einstein manifold if and only if base manifold is the space of constant sectional curvature 1 or 2.15 pagesDifferential Geometry53C25, 53D10Remarks on $η$-Einstein unit tangent bundlestext