This ebook bargains with Riemannian manifolds for which the nullity area of the curvature tensor has codimension . those manifolds are “semi-symmetric areas foliated by means of Euclidean leaves of codimension ” within the experience of Z I Szabó. The authors be aware of the wealthy geometrical constitution and particular descriptions of those striking areas. additionally parallel theories are constructed for manifolds of “relative conullity two”. This makes a bridge to a survey on curvature homogeneous areas brought by means of I M Singer. As an program of the most subject, fascinating hypersurfaces with variety quantity in Euclidean house are came upon, specifically these that are in the neighborhood inflexible or “almost rigid”. The unifying technique is fixing explicitly specific structures of nonlinear PDE.
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