共查询到20条相似文献,搜索用时 0 毫秒
1.
Yujen Shu 《Geometriae Dedicata》2009,138(1):151-172
In this article, I prove the following statement: Every compact complex surface with even first Betti number is deformation equivalent to one which admits an extremal Kähler metric. In fact, this extremal Kähler metric can even be taken to have constant scalar curvature in all but two cases: the deformation equivalence classes of the blow-up of \({\mathbb {P}_2}\) at one or two points. The explicit construction of compact complex surfaces with constant scalar curvature Kähler metrics in different deformation equivalence classes is given. The main tool repeatedly applied here is the gluing theorem of C. Arezzo and F. Pacard which states that the blow-up/resolution of a compact manifold/orbifold of discrete type, which admits cscK metrics, still admits cscK metrics. 相似文献
2.
A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kähler metric of constant scalar curvature on the blow-up according to Rollin and Singer (J. Eur. Math. Soc., 2004). We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus, we can produce numerous examples of Kähler surfaces of constant scalar curvature with circle or toric symmetry. 相似文献
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4.
Jaeman Kim 《Annals of Global Analysis and Geometry》2009,35(4):339-343
We prove that every irreducible Kähler manifold with harmonic Bochner curvature tensor and constant scalar curvature is Kähler–Einstein and that every irreducible compact Kähler manifold with harmonic Bochner curvature tensor and negative semi-definite Ricci tensor is Kähler–Einstein. 相似文献
5.
The definition of Schrödinger flow is proposed. It is indicated that the flow of ferromagnetic chain is actually Schrödinger flow of maps intoS 2, and that there exists a unique local smooth solution for the initial value problem of one-dimensional Schrödinger flow of maps into Kahler manifolds. In case the targets are Kähler manifolds with constant curvature, it is proved that one-dimensional Schrödinger flow admits a unique global smooth solution. 相似文献
6.
Let \({\cal O}\) be a nilpotent orbit in ?? where G is a compact, simple group and ? = Lie(G). It is known that \({\cal O}\) carries a unique G-invariant hyperKähler metric admitting a hyperKähler potential compatible with the Kirillov–Kostant–Souriau symplectic form. In this work, the hyperKähler potential is explicitly calculated when \({\cal O}\) is of cohomogeneity three under the action of G. It is found that such a structure lies on a one-parameter family of hyperKähler metrics with G-invariant Kähler potentials if and only if ? is Sp3, su6, So7, So12 or e7 and otherwise is the unique G-invariant hyperKähler metric with G-invariant Kähler potential. 相似文献
7.
In this note, we look at estimates for the scalar curvature of a compact, connected Riemannian manifold Mwhich are related to spin
c
Dirac operators.We show that one may not enlarge a Kähler metric with positiveRicci curvature without making smaller somewhere on M.More generally, if f: N M is an area-nonincreasing map of a certain topological type,then the scalar curvature k of Ncannot be everywhere larger than f.If k f, then N is isometric to M × F, where F possesses a parallel untwisted spinor.We also give explicit upper bounds for min for arbitrary Riemannian metrics on certainsubmanifolds of complex projective space.In certain cases, these estimates are sharp:we give examples where equality is obtained. 相似文献
8.
We discuss a class of complete Kähler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L 2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincaré inequality case and establish a vanishing theorem provided that the weighted function ρ is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincaré inequality. 相似文献
9.
Jaeman Kim 《Czechoslovak Mathematical Journal》2006,56(1):267-271
On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat. 相似文献
10.
Yuguang ZHANG 《数学年刊B辑(英文版)》2007,28(4):421-428
Compact Kähler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell’s work, if M is a compact Kähler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition \( \ifmmode\expandafter\tilde\else\expandafter\~\fi{M} \cong X_{1} \times \cdots \times X_{m} \), where X j is a Calabi-Yau manifold, or a hyperKähler manifold, or X j satisfies H 0(X j , Ω p ) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature Kähler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ∈ > 0, there exists a Kähler structure (J ∈, g ∈) on M such that the volume \({\text{Vol}}_{{g_{ \in } }} {\left( M \right)} < V\), the sectional curvature |K(g ∈)| < Λ2, and the Ricci-tensor Ric(g ∈)> ?∈g ∈, where V and Λ are two constants independent of ∈. Then the fundamental group of M is finite, and M is diffeomorphic to a complex manifold X such that the universal covering of X has a decomposition, \( \ifmmode\expandafter\tilde\else\expandafter\~\fi{X} \cong X_{1} \times \cdots \times X_{s} \), where X i is a Calabi-Yau manifold, or a hyperKähler manifold, or X i satisfies H 0(X i , Ω p ) = {0}, p > 0. 相似文献
11.
Jongsu Kim 《Mathematische Zeitschrift》2009,262(2):381-388
We show that every symplectic manifold of dimension ≥ 4 admits a complete compatible almost Kähler metric of negative scalar curvature. And we discuss the C 0-closure of the set of almost Kähler metrics of negative scalar curvature. Some local versions are also proved. 相似文献
12.
Jongsu Kim 《Annals of Global Analysis and Geometry》2008,33(2):115-136
We show that any closed symplectic four-dimensional manifold (M, ω) admits an almost Kähler metric of negative scalar curvature compatible with ω. 相似文献
13.
We derive a parabolic equation for the K?hler angle of a real surface evolving under the mean curvature flow in a K?hler-Einstein surface and show that a symplectic curve remains symplectic with the flow. Received March 29, 2000, Revised April 29, 2000, Accepted May 16, 2000 相似文献
14.
Paul-Andi Nagy 《Mathematische Zeitschrift》2006,254(1):199-218
Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as Kähler and hyperbolic geometries are concerned. In the second part of the paper, we give algebraic and topological obstructions to the existence of a geometrically 2-formal Kähler metric, at the level of the second cohomology group. A strong interaction with almost Kähler geometry is to be noted. In complex dimension 3, we list all the possible values of the second Betti number of a geometrically 2-formal Kähler metric. 相似文献
15.
We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below. 相似文献
16.
Myong-Hee Sung 《Annals of Global Analysis and Geometry》1997,15(6):509-518
We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface. 相似文献
17.
Włodzimierz Jelonek 《Annals of Global Analysis and Geometry》2009,36(2):143-159
The aim of this article is to classify compact Kähler manifolds with quasi-constant holomorphic sectional curvature. 相似文献
18.
本文给出了近K?hler球面S6中具有常数K?hler角和常数曲率的极小曲面的例子,同时证明了两个唯一性定理. 相似文献
19.
We show that every 4-dimensional anti-Kähler manifold is Einstein and locally symmetric. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat. 相似文献
20.
Róbert Szőke 《Acta Mathematica Hungarica》2006,111(1-2):77-79
Summary We show that an isometry between not locally hyperk?hler, locally irreducible K?hler manifolds is either holomorphic or antiholomorphic. 相似文献