Kaehler structures on $K_{\mathbf C}/(P,P)$

Lecture on Kaehler manifolds

Jacobi-Type Vector Fields on Kaehler Manifold

In this paper, we use the notion of Jacobi-type vector fields introduced in [5] to obtain a necessary and sufficient condition for a Kaehler manifold to be isometric to the complex space form (Cn, J, 〈, 〉), where J is the complex structure and 〈, 〉 is the Euclidean metric on Cn. Mathematics Subject Classification: 53C20, 53B21

Lectures on Geodesics in the Space of Kaehler Metrics, Lecture 3: Hrma, Hcma and Toric Kaehler Manifolds

It is very hard to find computable examples of geodesics in the space of Kaehler metrics. It seems that they come in two types: (i) geodesics of toric Kaehler metrics, the topic of Lecture 2; (iii) geodesics coming from special test configurations and Hele-Shaw flows. Besides Donaldson’s construction (reviewed in §1) there are not many examples of geodesic rays. Almost the only other explicit e...

On CR-Lightlike Product of an Indefinite Kaehler Manifold

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

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 ...