Almost isotropy-maximal manifolds of non-negative curvature

Dong, Zheting; Escher, Christine; Searle, Catherine

doi:10.1090/tran/9100

Almost isotropy-maximal manifolds of non-negative curvature
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by Zheting Dong, Christine Escher and Catherine Searle;

Trans. Amer. Math. Soc. 377 (2024), 4621-4645

DOI: https://doi.org/10.1090/tran/9100

Published electronically: May 17, 2024

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Abstract:

We extend the equivariant classification results of Escher and Searle for closed, simply connected, Riemannian $n$-manifolds with non-negative sectional curvature 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 any such manifold is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to three.

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