About topology of saddle submanifolds |
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Authors: | A Borisenko V Rovenski |
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Institution: | a Kharkov National University, Faculty of Mechanics and Mathematics, Geometry Department, Svobodi sq. 4, Kharkov, 61077, Ukraine b Department of Mathematics, Faculty of Science and Science Education, University of Haifa, Mount Carmel, Haifa, 31905, Israel |
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Abstract: | 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. |
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Keywords: | 53B25 53C40 |
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