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Nonnegatively curved Euclidean submanifolds in codimension two
We provide a classification of compact Euclidean submanifolds
with nonnegative sectional curvature, for . The classification is in terms of the induced metric (including the
diffeomorphism classification of the manifold), and we study the structure of
the immersions as well. In particular, we provide the first known example of a
nonorientable quotient
with nonnegative curvature. For the 3-dimensional case, we show that either the
universal cover is isometric to , or is
diffeomorphic to a lens space, and the complement of the (nonempty) set of flat
points is isometric to a twisted cylinder
. As a consequence we conclude that, if
the set of flat points is not too big, there exists a unique flat totally
geodesic surface in whose complement is the union of one or two twisted
cylinders over disks.Comment: Accepted for publication in Commentarii Mathematici Helvetic
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