JournalsdmVol. 26pp. 1889–1927

Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension

  • John Harvey

    Department of Mathematics, Swansea University, Fabian Way, Swansea, UK

  • Catherine Searle

    Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS 67260, USA
Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension $4$ cover
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Abstract

We classify positively curved Alexandrov spaces of dimension with an isometric circle action up to equivariant homeomorphism, subject to a certain additional condition on the infinitesimal geometry near fixed points which we conjecture is always satisfied.

As a corollary, we also classify positively curved Riemannian orbifolds of dimension with an isometric circle action.

Cite this article

John Harvey, Catherine Searle, Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension . Doc. Math. 26 (2021), pp. 1889–1927

DOI 10.4171/DM/860