Riemannian Manifolds Of Conullity Two

This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are &quote;semi-symmetric spaces foliated by Euclidean leaves of codimension two&quote; in the sense of Z I Szabo. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of &quote;relative conullity two&quote;. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or &quote;almost rigid&quote;. The unifying method is solving explicitly particular systems of nonlinear PDE.