# Remarks on $η$-Einstein unit tangent bundles - Mathematics > Differential Geometry

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Abstract: We study the geometric properties of the base manifold for the unit tangentbundle satisfying the $\eta$-Einstein condition with the standard contactmetric structure. One of the main theorems is that the unit tangent bundle of4-dimensional Einstein manifold, equipped with the canonical contact metricstructure, is $\eta$-Einstein manifold if and only if base manifold is thespace of constant sectional curvature 1 or 2.

Author: Y. D. Chai, S. H. Chun, J. H. Park, K. Sekigawa

Source: https://arxiv.org/