The proof of Gromoll-Walschap conjecture
Gui Mu
TL;DR
This paper proves the Gromoll-Walschap conjecture, confirming that no Riemannian foliations exist on compact negatively curved manifolds, thus resolving a long-standing open problem in differential geometry.
Contribution
It provides a definitive proof of the Gromoll-Walschap conjecture, establishing a key property of Riemannian foliations on negatively curved manifolds.
Findings
No Riemannian foliations on compact negatively curved manifolds
Confirms the Gromoll-Walschap conjecture
Advances understanding of geometric structures on curved manifolds
Abstract
It is conjectured that there are no Riemannian foliations on compact manifold of negative curvature by Gromoll-Walschap in \cite{DG}. In this note we give a positive answer.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds