arXiv subjects
Publications and source records attributed to Dennis Wulle.
We classify fixed point homogeneous Riemannian orbifolds with positive sectional curvature up to equivariant diffeomorphism. As a corollary we obtain a classification of positively curved orbifolds with maximal symmetry rank.
The present article explores the relationship between positive sectional curvature and the geometric and topological properties of Eschenburg $6$-orbifolds. First, we prove that positive sectional curvature imposes restrictions on the their singular sets, thereby confirming a conjecture posed by Florit and Ziller. Then we compute the orbifold cohomology rings for those with a specific singular locus. This reveals a distinctive behavior in the cohomology groups of positively curved Eschenburg orbifolds compared to their non-negatively curved counterparts. Furthermore, we compute the orbifold cohomology rings of all Eschenburg orbifolds.
In 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.