In this paper, we prove a theorem on convergence of Kähler-Ricci flow on a compact Kähler manifold M which admits a Kähler-Ricci soliton. A Kähler metric h is called a Kähler-Ricci soliton if its Kähler form ωh satisfies equation Ric(ωh)− ωh = LXωh, where Ric(ωh) is the Ricci form of h and LXωh denotes the Lie derivative of ωh along a holomorphic vector field X on M . As usual, we denote a Kähl...

In this paper the relations between the existence of Lagrangian fibration of Hyper-Kähler manifolds and the existence of the Large Radius Limit is established. It is proved that if the the rank of the second homology group of a Hyper-Kähler manifold N of complex dimension 2n ≥ 4 is at least 5, then there exists an unipotent element T in the mapping class group Γ(N) such that its action on the s...

In the paper we prove a factorization theorem for representations of fundamental groups of compact Kähler manifolds (Kähler groups) into solvable matrix groups. We apply this result to prove that the universal covering of a compact Kähler manifold with a residually solvable fundamental group is holomorphically convex.

It is well-known that the αG(M)-invariant introduced by Tian plays an important role in the study of the existence of Kähler-Einstein metrics on complex manifolds with positive first Chern class ([T1], [T2], [TY]). Based on the estimate of αG(M)-invariant, Tian in 1990 proved that any complex surface with c1(M) > 0 always admits a Kähler-Einstein metric except in two cases CP2#1CP2 and CP2#2CP2...

If a normalized Kähler-Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M , dimC M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.

Applying the methods developed in [3], in [4] we have constructed generalized CS attached to the Jacobi group G1 = H1 oSU(1, 1), based on the homogeneous Kähler manifold D 1 = H1/R × SU(1, 1)/U(1) = C 1 × D1. Here D1 denotes the unit disk D1 = {w ∈ C ; |w| < 1}, and Hn is the (2n + 1)-dimensional real Heisenberg-Weyl group with Lie algebra hn. In [4] we have also emphasized that, when expressed...

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kähler manifold. As a consequence we obtain several results on the structure of Kähler groups, i.e., the fundamental groups of compact Kähler manifolds.

We show that any non-Kähler, almost Kähler 4-manifold for which both the Ricci and the Weyl curvatures have the same algebraic symmetries as they have for a Kähler metric is locally isometric to the (only) proper 3-symmetric four-dimensional space. Mathematics Subject Classifications (2000): Primary 53B20, 53C25.

We construct geometric shrinkage priors for Kählerian signal filters. Based on the characteristics of Kähler manifold, an algorithm for finding the superharmonic priors is introduced. The algorithm is efficient and robust to obtain the Komaki priors. Several ansätze for the priors are also suggested. In particular, the ansätze related to Kähler potential are geometrically intrinsic priors to th...

The so-called Kodaira problem left open by this result asked whether more generally any compact Kähker manifold can be deformed to a projective complex manifold. Recently, we solved negatively this question by constructing, in any dimension n ≥ 4, examples of compact Kähler manifolds, which do not deform to projective complex manifolds, as a consequence of the following stronger statement conce...