On 1/4-pinched 4-dimensional Riemannian manifolds of negative curvature
The following interesting result is proved using integral formulae for characteristic numbers: Let M be a compact oriented 4-dimensional Riemannian manifold with sectional curvature, \(K_ M\), satisfying \(-1\leq K_ M\leq -1/4\). Then the signature \(\tau\) (M), and Euler characteristic, \(\chi\) (M), are related by \(| \tau (M)| \leq (1/3) \chi (M)\). Moreover, equality holds if and only if M is locally isometric to the complex hyperbolic plane.
scientific article; zbMATH DE number 3919236