Cohomogeneity one manifolds with quasipositive curvature-Reference-Cited by-同舟云学术

Cohomogeneity one manifolds with quasipositive curvature

Published:2023-11-25 Issue: Volume: Page:
ISSN:0025-5831
Container-title:Mathematische Annalen
language:en
Short-container-title:Math. Ann.

Author:

Wulle Dennis

Abstract

AbstractIn this paper, we give a classification of cohomogeneity one manifolds admitting an invariant metric with quasipositive sectional curvature except for two 7-dimensional families. The main result carries over almost verbatim from the classification results in positive curvature carried out by Verdiani and Grove, Wilking and Ziller. Three main tools used in the positively curved case that we generalized to quasipositively curved cohomogeneity one manifolds are Wilking’s Chain Theorem, the classification of positively curved fixed point homogeneous manifolds by Grove and Searle and the Rank Lemma.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00208-023-02766-9.pdf

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