2007/02/23 by W. Dunbar, Dunbar, W., S. Greenwald +5
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20
paper · pdf · doi:10.48550/arxiv.math/0702680
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arxiv created 2007/02/23 · arxiv updated 2009/12/01
Let G, a subset of O(4), act isometrically on the 3-sphere. In this article we calculate a lower bound for the diameter of the quotient spaces S3/G. We find it to be 1/2\arccos((tan((3 π)/(10)))/(√3)), which is exactly the value of the lower bound for diameters of the spherical space forms. In the process, we are also able to find a lower bound for diameters for the spherical Aleksandrov spaces, Sn/G, of cohomogeneities 1 and 2, as well as for cohomogeneity 3 (with some restrictions on the group type). This leads us to conjecture that the diameter of Sn/G is increasing as the cohomogeneity of the group G increases.