We topologically characterize negatively curved Riemannian manifolds which are of cohomogeneity two under the action of a compact Lie group of isometries.
"On topology of some Riemannian manifolds of negative curvature with a compact Lie group of isometries." Hokkaido Math. J. 44 (1) 81 - 89, February 2015. https://doi.org/10.14492/hokmj/1470052354