We construct a distance nonincreasing deformation retraction from a complete open manifold of nonnegative sectional curvature to a soul. Using this retraction, we prove that any two souls are isometric and also obtain a lower bound on the injectivity radius of such manifolds.
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Yim, JW. Distance nonincreasing retraction on a complete open manifold of nonnegative sectional curvature. Ann Glob Anal Geom 6, 191–206 (1988). https://doi.org/10.1007/BF00133039
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DOI: https://doi.org/10.1007/BF00133039