Compact 4-manifolds with harmonic Weyl tensor and nonnegative biorthogonal curvature
In this note we classify compact 4-manifolds with harmonic Weyl tensor and nonnegative biorthogonal curvature
math.DG↗
arXiv subjects
Ezio Araujo Costa
Publications and source records attributed to Ezio Araujo Costa.
The scalar curvature and the biorthogonal curvature: A pinching problem
The famous pinching problem says that on a compact simply connected $n$-manifold if its sectional curvature satisfies $K_{min} > (1/4)K_{max} > 0$, then the manifold is homeomorphic to the sphere. In [8, problem 12], S. T. Yau proposed the following problem: If we replace $K_{max}$ by the scalar curvature, can we deduce similar pinching theorems? In our present note we give an answer to this question in dimension $n = 4.$}
math.DG↗
A modified Yamabe invariant and a Hopf conjecture
In this paper we define the bi-orthogonal sectional curvature and we present two modified Yamabe invariants for compact 4-dimensional manifolds. In particular we obtained a relationship between one of these invariants and a Hopf conjecture.
math.DG↗