Existence of flat tori in analytic manifolds of nonpositive curvature

DOI10.24033/asens.1638zbMath0760.53032OpenAlexW2517277637MaRDI QIDQ3988726

Viktor Schroeder, Victor Bangert

Publication date: 28 June 1992

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1991_4_24_5_605_0

zbMATH Keywords

fundamental groupgeodesic flowclosed geodesicclosed \(k\)-flatflag of singular subflats

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Real-analytic and semi-analytic sets (14P15) Global Riemannian geometry, including pinching (53C20)

Related Items (14)

Polygonal complexes and combinatorial group theory ⋮ Nonpositively curved 2-complexes with isolated flats. ⋮ Ergodic geometry for non-elementary rank one manifolds ⋮ Regular elements in CAT(0) groups. ⋮ Regular combings, nonpositive curvature and the quasiconvexity of Abelian subgroups ⋮ On Non-hyperbolic Quasi-convex Spaces ⋮ On the geometric rank of homogeneous spaces of nonpositive curvature ⋮ Hopf-Tsuji-Sullivan dichotomy for quotients of Hadamard spaces with a rank one isometry ⋮ Tits geometry of cocompact real-analytic Hadamard manifolds of dimension 4 ⋮ On nonpositively curved compact Riemannian manifolds with degenerate Ricci tensor ⋮ Fat Flats in rank one manifolds ⋮ Isometry groups of non-positively curved spaces: discrete subgroups ⋮ On the generic nonexistence of rational geodesic foliations in the torus, Mather sets and Gromov hyperbolic spaces ⋮ Open problems and questions about geodesics

Cites Work

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• Geodesic Rigidity in Compact Nonpositively Curved Manifolds
• Existence of immersed tori in manifolds of nonpositive curvature.
• A Cusp Closing Theorem
• Manifolds of Negative Curvature
• Geodesic Flow in Certain Manifolds Without Conjugate Points
• Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature
• Invariant manifolds

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