23 research outputs found
Geometric realizations of Kaehler and of para-Kaehler curvature models
We show that every Kaehler algebraic curvature tensor is geometrically
realizable by a Kaehler manifold of constant scalar curvature. We also show
that every para-Kaehler algebraic curvature tensor is geometrically realizable
by a para-Kaehler manifold of constant scalar curvatur
Examples of signature (2,2) manifolds with commuting curvature operators
We exhibit Walker manifolds of signature (2,2) with various commutativity
properties for the Ricci operator, the skew-symmetric curvature operator, and
the Jacobi operator. If the Walker metric is a Riemannian extension of an
underlying affine structure A, these properties are related to the Ricci tensor
of A
The structure of the space of affine Kaehler curvature tensors as a complex module
We use results of Matzeu and Nikcevic to decompose the space of affine
Kaehler curvature tensors as a direct sum of irreducible modules in the complex
settin
Stanilov-Tsankov-Videv Theory
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