Classification of Einstein metrics on the product of an interval with a three-sphere

Details Classification of Einstein metrics on the product of an interval with a three-sphere Classification of Einstein metrics on the product of an interval with a three-sphere

2011-11-09

arxiv.org/abs/1111.2153v1

Mathematics

Differential Geometry

12 pages, no figures. Paper written in 2004

Scientific paper

We present a complete classification of Einstein metrics on the space M = I \times S^3, where I is the interval (0,l) or (0,\infty) or their closures, and we consider separate metric functions f and h (functions of I) for the base and fiber of the Hopf fibration S^1 -> S^3 -> S^2. All such metrics yielding smooth and complete manifolds are included and discussed. The results are surprisingly rich, including many well-known examples and several one-parameter families of metrics with a variety of geometries.

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