Transactions of the American Mathematical Society

Author(s): Luis Guijarro; Gerard Walschap
Journal: Trans. Amer. Math. Soc. 352 (2000), 55-69.
MSC (1991): Primary 53C20
Posted: March 8, 1999
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Abstract: We study geometric properties of the metric projection $\pi :M\to S$ of an open manifold

with nonnegative sectional curvature onto a soul

. $\pi$ is shown to be $C^{\infty }$ up to codimension 3. In arbitrary codimensions, small metric balls around a soul turn out to be convex, so that the unit normal bundle of

also admits a metric of nonnegative curvature. Next we examine how the horizontal curvatures at infinity determine the geometry of

, and study the structure of Sharafutdinov lines. We conclude with regularity properties of the cut and conjugate loci of

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Luis Guijarro
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Address at time of publication: Departamento de Matématicas, Universidad Autónoma de Madrid, Madrid, Spain
Email: luis.guijarro@uam.es

Gerard Walschap
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: gwalschap@ou.edu

DOI: 10.1090/S0002-9947-99-02237-0
PII: S 0002-9947(99)02237-0
Keywords: Sharafutdinov retraction, soul, pseudosoul, convexity
Received by editor(s): August 18, 1997
Posted: March 8, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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