Closed q-convex hypersurfaces in (n+1)-dimensional Riemannian manifolds satisfy vanishing theorems for Betti numbers under lower bounds on curvature operator eigenvalues, implying they are rational homology spheres with finite fundamental group when convex or pinched.
Sacksteder,On hypersurfaces with no negative sectional curvatures, Amer
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
On $q$-convex hypersurfaces in Riemannian manifolds
Closed q-convex hypersurfaces in (n+1)-dimensional Riemannian manifolds satisfy vanishing theorems for Betti numbers under lower bounds on curvature operator eigenvalues, implying they are rational homology spheres with finite fundamental group when convex or pinched.