The soul at infinity in dimension 4

Walschap, Gerard

doi:10.1090/S0002-9939-1991-1049852-X

The soul at infinity in dimension $4$
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Proc. Amer. Math. Soc. 112 (1991), 563-567 Request permission

Abstract:

It is shown that $4$-dimensional open manifolds with nonnegative sectional curvature whose fibers are totally geodesic are metrically rigid. For arbitrary dimension, one also concludes that the curvature is in a sense maximal at the soul.

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