4 problems

0 votes0 replies0 views
Grove–Ziller conjecture on non-negative curvature of cohomogeneity one manifolds
Grove–Ziller conjecture. Any cohomogeneity one manifold admits a Riemannian metric with non-negative sectional curvature.
Conjecturerefutedcohomogeneity-one-manifolds nonnegative-curvature riemannian-geometryarXiv posted 2 days ago
0 votes0 replies0 views
Diagonal Ricci flow conjecture for cohomogeneity one manifolds
Let $(M,\mathsf{G})$ be a cohomogeneity one manifold, let $\mathcal{B}$ be a stably Ricci-diagonal basis for it, and let $\mathrm{g}_0$ be a metric on $M$ that is diagonal with res…
Conjectureopencohomogeneity-one-manifolds ricci-flow riemannian-geometryarXiv posted 2 days ago
0 votes0 replies1 view
Foscolo–Haskins conjecture on cohomogeneity-one nearly Kähler six-manifolds
A compact nearly Kähler manifold is cohomogeneity one if it is equipped with an isometric action of a compact Lie group whose generic orbits have codimension one. Foscolo–Haskins c…
Conjectureopencohomogeneity-one-manifolds nearly-kahler-geometry riemannian-geometryarXiv posted 2 days ago
0 votes0 replies0 views
Positive curvature conjecture for the manifolds $P_k$ and $Q_k$
Positive curvature conjecture for $P_k$ and $Q_k$ . All manifolds $P_k$ and $Q_k$ admit metrics of positive curvature.
Conjectureopencohomogeneity-one-manifolds orbifolds positive-curvaturearXiv posted 2 days ago

Grove–Ziller conjecture on non-negative curvature of cohomogeneity one manifolds