By Peter B Gilkey

ISBN-10: 9810247524

ISBN-13: 9789810247522

A important challenge in differential geometry is to narrate algebraic homes of the Riemann curvature tensor to the underlying geometry of the manifold. the whole curvature tensor is normally rather tricky to house. This publication offers effects concerning the geometric effects that stick with if a number of usual operators outlined when it comes to the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and better order generalizations) are assumed to have consistent eigenvalues or consistent Jordan common shape within the applicable domain names of definition.

The e-book offers algebraic preliminaries and diverse Schur kind difficulties; bargains with the skew-symmetric curvature operator within the genuine and complicated settings and offers the type of algebraic curvature tensors whose skew-symmetric curvature has consistent rank 2 and incessant eigenvalues; discusses the Jacobi operator and a better order generalization and provides a unified remedy of the Osserman conjecture and similar questions; and establishes the consequences from algebraic topology which are important for controlling the eigenvalue buildings. an intensive bibliography is equipped. effects are defined within the Riemannian, Lorentzian, and better signature settings, and lots of households of examples are displayed.