Kouei Sekigawa, Hiroshi Suga, Lieven Vanhecke
Four-dimensional curvature homogeneous spaces

Abstract:We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.

Keywords: Riemannian manifold, curvature homogeneous spaces, homogeneous spaces
AMS Subject Classification: 53C20, 53C30

PDF