Almost Isotropy-Maximal Manifolds of Non-negative Curvature

Zheting Dong; Christine Escher; Catherine Searle

Almost Isotropy-Maximal Manifolds of Non-negative Curvature

Differential Geometry 2023-11-28 v3

Authors: Zheting Dong , Christine Escher , Catherine Searle

Abstract

We extend the equivariant classification results of Escher and Searle for closed, simply connected, non-negatively curved Riemannian $n$ -manifolds admitting isometric isotropy-maximal torus actions to the class of such manifolds admitting isometric strictly almost isotropy-maximal torus actions. In particular, we prove that such manifolds are equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to three.

Keywords

non-negative curvature isotropy-maximal torus action almost isotropy-maximal equivariant classification riemannian manifold

Cite

@article{arxiv.1811.01493,
  title  = {Almost Isotropy-Maximal Manifolds of Non-negative Curvature},
  author = {Zheting Dong and Christine Escher and Catherine Searle},
  journal= {arXiv preprint arXiv:1811.01493},
  year   = {2023}
}

Comments

Section 3 rewritten to streamline arguments. Remark 1.1 from previous version is now Theorem B. To appear in Transactions of the AMS

Almost Isotropy-Maximal Manifolds of Non-negative Curvature

Abstract

Keywords

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