Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606654 | Differential Geometry and its Applications | 2007 | 14 Pages |
Abstract
The (k,ε)(k,ε)-saddle (in particular, k -saddle, i.e. ε=0ε=0) submanifolds are defined in terms of eigenvalues of the second fundamental form. This class extends the class of submanifolds with extrinsic curvature bounded from above, i.e. ⩽ε2⩽ε2 (in particular, non-positive) and small codimension. We study s-connectedness and (co)homology properties of compact submanifolds with ‘small’ normal curvature and saddle submanifolds in Riemannian spaces of positive (sectional or qth Ricci) curvature. The main results are that a submanifold or the intersection of two submanifolds is s-connected under some assumption. By the way, theorems by T. Frankel and some recent results by B. Wilking, F. Fang, S. Mendonça and X. Rong are generalized.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
A. Borisenko, V. Rovenski,