Abstract:
In addition to a systematic, broad-based introduction to the field of algebraic curvature operators and the Sharp-product, this text provides a large number of new (algebraic) results, which can be seen in the context of the dynamics of Ricci flow on manifolds. For example, it is shown that the first Bianchi identity follows from the Böhm-Wilking identity. Moreover, the irreducible decomposition of the Ricci vector field is computed. Further, the text is concerned with the dynamics of the vector field Ricci on the space of algebraic curvature operators and a splitting theorem for equilibrium positions of the normalized Ricci vector field is proved.