Stanilov-Tsankov-Videv Theory

Abstract

We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (9)

• Pseudo-Riemannian Jacobi-Videv Manifolds
• Conformally Osserman manifolds and self-duality in Riemannian geometry
• Determination of the structure of algebraic curvature tensors by means of Young symmetrizers
• Examples of signature (2,2) manifolds with commuting curvature operators
• The spectral geometry of the Weyl conformal tensor
• Completeness, Ricci blowup, the Osserman and the conformal Osserman condition for Walker signature (2,2) manifolds
• Four-dimensional Riemannian manifolds with commuting higher order Jacobi operators
• Puffini-Videv Models and Manifolds
• Jacobi--Tsankov manifolds which are not 2-step nilpotent

Cited by in corpus (2)

• Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups
• The classification of simple Jacobi--Ricci commuting algebraic curvature tensors