强Khler-Finsler流形上(p,q)形式的中值Laplace算子(英文)

本文给出了强Khler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Khler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Khler-Finsler流形上的逆变密切Khler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Khler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。     

强Kaehler-Finsler流形上（p，q）形式的中值Laplace算子

本文给出了强Kaehler-Finsler流形上中值Laplace算子的一些性质，如自伴性质，散度形式等。与Kaehler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同，作者利用强Kaehler-Finsler流形上的逆变密切Kaehler度量作为密度函数定义了流形上的逐点内积和整体内积，并定义了强Kaehler-Finsler流形上的Hodge-Laplace算子，它可看作函数情形中值Laplace算子的推广。     

Finsler流形上的Laplace算子

该文对Finsler流形上的微分式定义了整体内积，进而引入δ算子和Laplace算子。该文还给出了δ算子的局部坐标表达式并且证明了Laplace算子可以看成是Riemann流形上Laplace算子在Finsler流形上的扩张。     

用线性算子定义的亚纯P叶函数子类(英文)

本文引进用算子定义的亚纯 p叶函数新子类 ,建立了包含关系 ,讨论了类中函数的积分算子性质 ,所得结果拓广了 [2 ]、[3 ]、[4]、[5 ]中的相应结果 .     

Riemann流形上Laplace算子第一特征值的一点注记

本文研究了黎曼流形上Laplace算子的第一特征值,利用流形的测地球上的Sobolev常数进行讨论并进行Moser迭代,得到闭的黎曼流形上Laplace算子第一特征值的一个下界估计.     

方程△g-aKg=0无正函数解的充分条件

Fischer-Colbrie和Schoen曾在1980年研究过复平面中单位圆盘当赋予某个完备度量时,方程Δg-aKg=0在其上无正函数解的充分条件,并将其结果应用到三维非负数量曲率流形中完备稳定的极小曲面上.这里Δ是Laplace算子,K为高斯曲率,a是常数,g是所讨论的单位圆盘上的函数.本文给出了此方程在该圆盘上无正函数解的一个更弱的充分条件.     

K(a)hler流形上的Lagrange力学

讨论了K(a)hler流形上的Lagrange力学,并给出Lagrange算子、Lagrange方程、作用泛函、Hamilton原理和Hamilton方程等复的数学形式.     

Finsler流形上的Laplace比较定理和有界估计(英文)

本文研究了Finsler流形上的距离函数的Laplacian.利用指标引理和文献[4]中主要方法,获得了Ricci曲率有函数下界的Laplacian比较定理,改进了文献[6]和文献[7]的相关结果.     

(ω)性质的判定

利用新定义的谱集,刻画了Hilbert空间上有界线性算子满足(ω_1)性质和(ω)性质的等价条件.另外,利用该谱集,对算子函数的(ω)性质进行了判定.     

内积函数的表示

本文首先定义了内积函数,这个概念推广了内积的定义.然后定义了Hilbert空间（H,〈·,·〉）上由严格正算子A诱导的范数,这个范数与由〈·,·〉诱导的范数是等价的.进一步,证明了所有的内积函数与线性有界的严格正算子全体之间存在一一对应关系.     

Hodge decomposition theorem on strongly K(a)hler Finsler manifolds

Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (θ)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M, F) is a compact strongly K(a)hler Finsler manifold, we define a (θ)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in K(a)hler manifolds is still true in the more general compact strongly K(a)hler Finsler manifolds.     

乘积复流形上的Szabó度量

设(M_1,α),(M_2,β)均为Hermitian流形,本文证明了积流形M_1×M_2上的复Szabó度量F_ε是Berwald度量,且当α,β为K(?)hler度量时,F_ε是强Kahler-Finsler度量,此外本文还给出了F_ε的全纯曲率的显式表达式．     

乘积复流形上的Szabó度量

设(M_1,α),(M_2,β)均为Hermitian流形,本文证明了积流形M_1×M_2上的复Szabó度量F_ε是Berwald度量,且当α,β为K(?)hler度量时,F_ε是强Kahler-Finsler度量,此外本文还给出了F_ε的全纯曲率的显式表达式．     

Affinely equivalent Khler-Finsler metrics on a complex manifold

The purpose of the present paper is to investigate affinely equivalent Khler-Finsler metrics on a complex manifold.We give two facts (1) Projectively equivalent Khler-Finsler metrics must be affinely equivalent;(2) a Khler-Finsler metric is a Khler-Berwald metric if and only if it is affinely equivalent to a Khler metric.Furthermore,we give a formula to describe the affine equivalence of two weakly Khler-Finsler metrics.     

Affinely equivalent K?hler-Finsler metrics on a complex manifold

The purpose of the present paper is to investigate affinely equivalent K?hler-Finsler metrics on a complex manifold. We give two facts (1) Projectively equivalent K?hler-Finsler metrics must be affinely equivalent; (2) a K?hler-Finsler metric is a K?hler-Berwald metric if and only if it is affinely equivalent to a K?hler metric. Furthermore, we give a formula to describe the affine equivalence of two weakly K?hler-Finsler metrics.     

Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J, K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics. We prove a quaternionic analogue of A. D. Aleksandrov and ChernLevine-Nirenberg theorems.     

Examples of non-Kähler Hamiltonian torus actions

An important question with a rich history is the extent to which the symplectic category is larger than the K?hler category. Many interesting examples of non-K?hler symplectic manifolds have been constructed [T] [M] [G]. However, sufficiently large symmetries can force a symplectic manifolds to be K?hler [D] [Kn]. In this paper, we solve several outstanding problems by constructing the first symplectic manifold with large non-trivial symmetries which does not admit an invariant K?hler structure. The proof that it is not K?hler is based on the Atiyah-Guillemin-Sternberg convexity theorem [At] [GS]. Using the ideas of this paper, C. Woodward shows that even the symplectic analogue of spherical varieties need not be K?hler [W]. Oblatum IX-1995 & 3-III-1997     

K(a)hler Manifolds with Almost Non-negative Ricci Curvature

Compact K(a)hler manifolds with semi-positive Ricci curvature have been investigated by various authors. From Peternell's work, if M is a compact K(a)hler n-manifold with semi-positive Ricci curvature and finite fundamental group, then the universal cover has a decomposition (M) ≌ X1 × … × Xm, where Xj is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xj satisfies Ho(Xj,Ωp) = 0. The purpose of this paper is to generalize this theorem to almost non-negative Ricci curvature K(a)hler manifolds by using the Gromov-Hausdorff convergence. Let M be a compact complex n-manifold with non-vanishing Euler number. If for any ε ＞ 0, there exists a K(a)hler structure (Je,ge) on M such that the volume Volge(M) ＜ V, the sectional curvature |K(gε)| ＜ Λ2, and the Ricci-tensor Ric(gε)＞ -εgε, where ∨ and Λ are two constants independent of ε. 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, (X) ≌ X1 × … × Xs, where Xi is a Calabi-Yau manifold, or a hyperK(a)hler manifold, or Xi satisfies Ho(Xi, Ωp) = {0}, p ＞ 0.     

Traceless component of the conformal curvature tensor in Kähler manifold

We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension ? 4, and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on p (0 ? p ? 2)-forms on the manifold by using the traceless component.