Scalar curvature rigidity of the four-dimensional sphere

Key Points

• The research aims to establish isometry conditions for four-dimensional Riemannian manifolds based on scalar curvature constraints.
• Examined a four-dimensional closed connected oriented Riemannian manifold with scalar curvature minimum of 12.
• Applied a smooth distance non-increasing map from the manifold to the unit four-sphere.
• Proved the isometry condition without relying on the spin structure.
• Showed that any such map with non-zero degree is an isometry.
• Demonstrated the removal of spin conditions that were previously necessary in similar theorems.
• Established a generalization of Llarull’s scalar curvature rigidity theorem.

Abstract