About topology of saddle submanifolds
About topology of saddle submanifolds
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DOI：
10.1016/j.difgeo.2006.08.001
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发表时间：
2007-04
影响因子：
0.5
通讯作者：
A. Borisenko;V. Rovenski
中科院分区：
文献类型：
--
作者：
A. Borisenko;V. Rovenski
The (k,ε)-saddle (in particular, k-saddle, i.e. ε=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(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.
