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<p>We prove that any dual leaf <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{\#}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mo>#</mo> </msup> </math></EquationSource> </InlineEquation> of a simply connected, complete nonnegatively curved polar manifold <i>M</i> is totally geodesic and closed in <i>M</i>, and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^{\#}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mo>#</mo> </msup> </math></EquationSource> </InlineEquation> is itself a complete nonnegatively curved polar manifold. Furthermore, the dual foliation on <i>M</i> induces a Riemannian submersion with totally geodesic fibers from <i>M</i> to a homogeneous space.</p>

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The dual foliation of polar actions on nonnegatively curved manifolds

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Yi Shi

摘要

We prove that any dual leaf \(L^{\#}\) L # of a simply connected, complete nonnegatively curved polar manifold M is totally geodesic and closed in M, and \(L^{\#}\) 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.