Remarks on $η$-Einstein unit tangent bundles

Details Remarks on $η$-Einstein unit tangent bundles Remarks on $η$-Einstein unit tangent bundles

2007-08-10

arxiv.org/abs/0708.1400v1

Mathematics

Differential Geometry

15 pages

Scientific paper

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $\eta$-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 $\eta$-Einstein manifold if and only if base manifold is the space of constant sectional curvature 1 or 2.

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