Abstract
We prove that an open nonnegatively curved manifold Mn with soul Sk splits isometrically as S × ℝ2−k if (and only if) the holonomy group of the normal bundle NS is trivial.
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Strake, M. A splitting theorem for open nonnegatively curved manifolds. Manuscripta Math 61, 315–325 (1988). https://doi.org/10.1007/BF01258442
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DOI: https://doi.org/10.1007/BF01258442