Extrinsci radius pinching in space forms of nonnegative sectional curvature

Details Extrinsci radius pinching in space forms of nonnegative sectional curvature Extrinsci radius pinching in space forms of nonnegative sectional curvature

2006-09-18

arxiv.org/abs/math/0609492v1

Mathematische Zeitschrift 258, 1 (2008) 227-240

Mathematics

Differential Geometry

16 pages

Scientific paper

We give new estimates for the extrinsic radius of compact hypersurfaces of
the Euclidean space and the open hemisphere in terms of high order mean
curvatures. Then we prove pinching results corresponding to theses estimates.
We show that under a suitable pinching condition, the hypersurface is
diffeomorphic and almost isometric to a geodesic hypersphere.

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