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 "e;semi-symmetric spaces foliated by Euclidean leaves of codimension two"e; 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 "e;relative conullity two"e;. 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 "e;almost rigid"e;. The unifying method is solving explicitly particular systems of nonlinear PDE.