Explicit constructions of closed even-dimensional manifolds with positive mixed sectional curvature on 1D totally geodesic circle foliations provide counterexamples to Toponogov's question by violating the predicted Ferus-Adams leaf dimension bound.
Rovenski,The partial Ricci flow for foliations, inGeometry and Its Applica- tions, Springer Proc
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Closed counterexamples to Toponogov's question on mixed curvature
Explicit constructions of closed even-dimensional manifolds with positive mixed sectional curvature on 1D totally geodesic circle foliations provide counterexamples to Toponogov's question by violating the predicted Ferus-Adams leaf dimension bound.