ISSN:
1570-5846
Keywords:
the second fundamental form
;
Ricci curvature
;
integral homology
;
stable currents.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold Mn in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of Mn has a positive lower bound. Making use of the Lawson–Simons formula for the nonexistence of stable k-currents, we eliminate Hk (Mn, Z) for all 1 ` k ` n − 1.We then observe that the fundamental group of Mn is trivial. It should be emphasized that our result is optimal.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1000189116072
Permalink