The dual foliation of polar actions on nonnegatively curved manifolds

2025/09/29 by Shi, Yi
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.24155

Abstract

We prove that any dual leaf L^# of a simply connected, complete nonnegatively curved polar manifold M is totally geodesic and closed in M, and L^# is itself a complete nonnegatively curved polar manifold. Furthermore, the dual foliation on M induces a Riemannian submersion with totally geodesic fibers from M to a homogeneous space.

Citations

• Smoothness of submetries
• A Weyl's Law for Singular Riemannian Foliations with Applications to Invariant Theory
• On the topology of leaves of singular Riemannian foliations
• On the completeness of dual foliations on nonnegatively curved symmetric spaces
• Polar foliations on symmetric spaces and the mean curvature flow
• Laplacian algebras, manifold submetries and the Inverse Invariant Theory\n Problem
• On Riemannian Foliations over Positively Curved Manifolds
• Algebraic nature of singular Riemannian foliations in spheres
• Hyperpolar actions on reducible symmetric spaces
• The dual foliation of some singular Riemannian foliations
• Low Dimensional Polar Actions
• Clifford algebras and new singular Riemannian foliations in spheres
• Differentiable classification of 4-manifolds with singular Riemannian foliations
• Extending tensors on polar manifolds
• Twisted submersions in nonnegative sectional curvature
• Polar manifolds and actions
• Tits Geometry and Positive Curvature
• Polar foliations on symmetric spaces
• Hyperpolar homogeneous foliations on symmetric spaces of noncompact type
• A duality theorem for Riemannian foliations in nonnegative sectional curvature
• Coisotropic and polar actions on compact irreducible Hermitian symmetric spaces

Related

• Twisted submersions in nonnegative sectional curvature
• A duality theorem for Riemannian foliations in nonnegative sectional curvature
• Geometric resolution of singular Riemannian foliations
• Singular Riemannian Foliations on Nonpositively Curved Manifolds
• On the completeness of dual foliations on nonnegatively curved symmetric spaces