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math.DG2021★ 1 cited
Geography of pinched four-manifolds
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We prove several new restrictions on the Euler characteristic and signature of oriented 4-manifolds with (positively or negatively) pinched sectional curvature. In particular, we s…
math.DG2019★ 6 cited
Convex Algebraic Geometry of Curvature Operators
Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes
We study the structure of the set of algebraic curvature operators satisfying a sectional curvature bound under the light of the emerging field of Convex Algebraic Geometry. More p…