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Homotopy connectedness theorems for submanifolds of Sasakian manifolds. (English) Zbl 1329.53081

Summary: The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal \(q\)-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and \((k,\varepsilon)\)-saddle submanifolds in Sasakian manifolds with positive transversal \(q\)-Ricci curvature are proved by using the weak (\(\varepsilon\)-)asymptotic index. As a corollary, a Frankel type theorem is proved.

MSC:

53C40 Global submanifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
55Q05 Homotopy groups, general; sets of homotopy classes
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