The Geometry Of Walker Manifolds

This book is intended to be a non-technical introduction to Walker manifolds. Topics covered include curvature models, Jacobi and the skew symmetric curvature operators, and examine questions related to the spectral geometry or commutativity properties of these operators. Also introduced are basic manifold theory, pseudo-Riemannian geometry, pseudo-Hermitian and para-Hermitian structures. Walker coordinates, several different families of Walker manifolds, and the theory of Riemannian extensions are also covered in detail. Contents: 1. Basic Algebraic Notions 2. Basic Geometrical Notions 3. Walker Structures 4. Three Dimensional Lorentzian Walker Manifolds 5. Four Dimensional Walker Manifolds 6. The spectral geometry of the curvature tensor 7. Hermitian geometry 8. Special Walker manifolds