A connectedness principle in the geometry of positive curvature

DOI10.4310/CAG.2005.v13.n4.a2zbMath1131.53306OpenAlexW1996093425MaRDI QIDQ819546

Xiaochun Rong, Sérgio J. Mendonça, Fu-Quan Fang

Publication date: 29 March 2006

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.cag/1144094669

zbMATH Keywords

totally geodesic submanifoldstotally geodesic immersionsSynge theorem

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

Local symmetry rank bound for positive intermediate Ricci curvatures ⋮ On \((k,\varepsilon)\)-saddle submanifolds of Riemannian manifolds ⋮ Homotopy connectedness theorems for submanifolds of Sasakian manifolds ⋮ Complete submanifolds of manifolds of negative curvature ⋮ Knots in Riemannian manifolds ⋮ Unnamed Item ⋮ On positive quaternionic Kähler manifolds with \(b_{4} = 1\) ⋮ Theorems of Barth-Lefschetz type in Sasakian geometry ⋮ On positive quaternionic Kähler manifolds with certain symmetry rank ⋮ Some connectedness problems in positively curved Finsler manifolds ⋮ Theorems of Barth-Lefschetz type and Morse theory on the space of paths in homogeneous spaces ⋮ Collapsed 5-manifolds with pinched positive sectional curvature ⋮ Complete submanifolds with bounded mean curvature in a Hadamard manifold

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