GEOMETRIC REALIZATIONS OF KAEHLER AND OF PARA-KAEHLER CURVATURE MODELS

Geometric Realizations of Hermitian Curvature Models

We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant ⋆-scalar curvature which satisfies the Kaehler condition at the point in question.

Lecture on Kaehler manifolds

Instantons and Kaehler Geometry of Nilpotent Orbits

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical oscillator, a polarization of the symplectic orbit invariant under the maximal compact subgroup is required. In this paper, we explain how such a polarizatio...

A Hitchin-kobayashi Correspondence for Kaehler Fibrations

Let X be a compact Kaehler manifold and E → X a principalK bundle, where K is a compact connected Lie group. Let A 1,1 be the set of connections on E whose curvature lies in Ω(E ×Ad k). Let k = Lie(K), and fix on k a nondegenerate biinvariant bilinear pairing. This allows to identify k ≃ k∗. Let F be a Kaehler left K-manifold and suppose that there exists a moment map μ : F → k∗ for the action ...

Hopf hypersurfaces in nearly Kaehler 6-sphere

We obtain a characterization for a compact Hopf hypersurface in the nearly Kaehler sphere S using a pinching on the scalar curvature of the hypersurface. It has been also observed that the totally geodesic sphere S in S has induced Sasakian structure as a hypersurface of the nearly Kaehler sphere S. M.S.C. 2000: 53C20, 53C45.