Quaternionic Kaehler manifolds and a curvature characterization of two-point homogeneous spaces

Algebras of Curvature Forms on Homogeneous Manifolds

Let C(X) be the algebra generated by the curvature two-forms of standard holomorphic hermitian line bundles over the complex homogeneous manifold X = G/B. The cohomology ring of X is a quotient of C(X). We calculate the Hilbert polynomial of this algebra. In particular, we show that the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. We...

Lecture on Kaehler manifolds

Homogeneous symplectic manifolds with Ricci - type curvature

We consider invariant symplectic connections ∇ on homogeneous symplectic manifolds (M, ω) with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible with the symplectic structure. If M is compact with finite fundamental group then (M...

On curvature homogeneous 4D Lorentzian manifolds

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH3 for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, CH2 manifolds that are not homogeneous. PACS numbers: 04.20, 02.40 AMS classification scheme numbers: 53C50

Special geometry, cubic polynomials and homogeneous quaternionic spaces

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain N = 2 supergravity theories, where dimensional reduction induces a mapping between special real, Kähler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the Kähler and quaternionic manifolds in homogeneous holomorphic f...