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arXiv · 1111.2153

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

Curtis T. Asplund·Brian Krummel·Evan Merrell·Robert Rachal·DaGang Yang
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Abstract

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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Curtis T. Asplund, Brian Krummel, Evan Merrell, Robert Rachal, DaGang Yang. 2011-11-09. Classification of Einstein metrics on the product of an interval with a three-sphere. https://arxiv.org/abs/1111.2153

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