2011/11/09 by Curtis T. Asplund, Asplund, Curtis T., Brian Krummel +7
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1111.2153
12 pages, no figures. Paper written in 2004
arxiv created 2011/11/09 · arxiv updated 2011/11/10
We present a complete classification of Einstein metrics on the space M = I × S3, where I is the interval (0,l) or (0,∞) or their closures, and we consider separate metric functions f and h (functions of I) for the base and fiber of the Hopf fibration S1 -> S3 -> S2. 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.