复Finsler流形上的Hodge-Laplace算子

本文定义了强拟凸复Finsler流形上的Hodge-Laplace算子,并给出其水平部分的局部坐标表示．     

关于曲面的切球丛的两点注记

本文讨论了曲面的切球丛的黎曼几何性质。证明了如下定理1 设(V,g)是2-维黎曼流形,(T(?)V,(?))是 V 上的切球丛,(?)为 Sasaki 度量,那么1)如果(T(?)V,(?))有正的截面曲率则 V 的 Gauss 曲率 k 必满足:0相似文献   

关于复Finsler流形的一个注记

设(M,G)为n维复Finsler流形,TM为M的全纯切丛,得到了TM上的Hermite度量hTM=G(-ij)(z,v)dzi(×)d(-z)j+G(-ij)(z,v)δvi(×)δ(-v)j为K(a)hler度量的充要条件是M为全纯曲率为0的Kahler流形,其中G(-ij)=(а)2G/(а)vi(а)(-v)j,1≤i,j≤n.推广了Cao-Wong的某些结果.     

Stein流形上全纯函数积分公式的拓广

得到了Stein流形上一种全纯函数的积分式，这种公式的特点含有可供选择的参数m≥2的整数，当m=2时即为Stein流形上全纯函数的方B-M公式．     

六维近凯勒流形的Kodaira维数

本文主要研究了六维近凯勒流形的典范丛和Kodaira维数.证明了六维严格近凯勒流形的典范丛是拟全纯平凡的,从而其Kodaira维数为0.特别地,证明了三维复射影空间CP3具有Kodaira维数不为-∞的近复结构.对于齐性的六维严格近凯勒流形,具体构造了它们典范丛的整体生成元.证明了齐性近凯勒流形F3和CP3的Hodge...     

靶流形为齐次流形的弱次椭圆Q调和映射的正则性

该文证明了靶流形为齐次流形的弱次椭圆Q调和映射是内部正则的，这里Q是定义域的 齐次维数。这一结果推广了Hajlasz和Strzelecki的相应结果[2].作为推论得到了靶流形为齐次流形的p维p调和映射的正则性.     

广义Kuramoto—Sivashinsky型方程惯性流形的存在性

本对一类广义Kuramoto-Sivashisky型方程证明了惯性流形的存在性，并对其维数作了估计同时研究了该方程的不变锥性质和轨线的强挤压性。     

双挠积复Finsler流形的局部对偶平坦性

设(M₁,F₁)和(M₂,F₂)是两个强凸的复Finsler流形,λ₁和λ₂是乘积流形M=M₁×M₂上的光滑实值函数,双挠积复Finsler流形(M₁×(λ₁,λ₂) M2,F)是在乘积流形上赋予了复Finsler度量F²=λ₁²F₁²+λ₂²F₂²的复Finsler流形.本文给出了双挠积复Finsler流形是局部对偶平坦流形的充要条件.     

仿射联络空间切丛之间的映射─—纪念导师吴光磊教授

本文依据Ｄｏｍｂｒｏｗｓｋｉ在仿射联络空间切丛上引进的近复结构，证明了：两个仿射联络空间之间的光滑映射的切映射保持近复结构不变的充分必要条件是该映射为全测地映射．     

复射影曲线上特殊线丛的射影正规性

本文给出复射影曲线上特殊线丛正规生成的一系列充分条件.     

Geometry of the Second-Order Tangent Bundles of Riemannian Manifolds

Let (M,g) be an n-dimensional Riemannian manifold and T2M be its secondorder tangent bundle equipped with a lift metric (g).In this paper,first,the authors construct some Riemannian almost product structures on (T2M,(g)) and present some results concerning these structures.Then,they investigate the curvature properties of (T2M,(g)).Finally,they study the properties of two metric connections with nonvanishing torsion on (T2 M,(g)):The H-lift of the Levi-Civita connection of g to T2 M,and the product conjugate connection defined by the Levi-Civita connection of (g) and an almost product structure.     

On Tangent Sphere Bundles with Small or Large Constant Radius

For a Riemannian manifold M, we determine somecurvature properties of a tangent sphere bundleT _r M endowed with the induced Sasaki metric in the case when the constantradius r > 0 of the tangent spheres is either sufficientlysmall or sufficiently large.     

On Manifolds Whose Tangent Bundle is Big and 1-Ample

A line bundle over a complex projective variety is called bigand 1-ample if a large multiple of it is generated by globalsections and a morphism induced by the evaluation of the spanningsections is generically finite and has at most 1-dimensionalfibers. A vector bundle is called big and 1-ample if the relativehyperplane line bundle over its projectivisation is big and1-ample. The main theorem of the present paper asserts that any complexprojective manifold of dimension 4 or more, whose tangent bundleis big and 1-ample, is equal either to a projective space orto a smooth quadric. Since big and 1-ample bundles are ‘almost’ample, the present result is yet another extension of the celebratedMori paper ‘Projective manifolds with ample tangent bundles’(Ann. of Math. 110 (1979) 593–606). The proof of the theorem applies results about contractionsof complex symplectic manifolds and of manifolds whose tangentbundles are numerically effective. In the appendix we re-provethese results. 2000 Mathematics Subject Classification 14E30,14J40, 14J45, 14J50.     

一般Hopf曲面上向量丛的结构

得到了非主Hopf曲面上连续复向量丛全纯结构的存在性及可滤性问题的充要条件.     

关于切丛和单位切球丛的度量的一个注记

本文在黎曼流形$(M,g)$的切丛$TM$ 上研究与参考文献[10]中平行的一类度量$G$以及相容的近复结构$J$.证明了切丛$TM$关于这些度量和相应的近复结构是局部共形近K\"{a}hler流形,并且把这些结构限制在单位切球丛上得到了切触度量结构的新例子.     

Unit Tangent Sphere Bundles with Constant Scalar Curvature

As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.     

Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of a Riemannian Manifold

In this paper we study a Riemannian metric on the tangent bundle T(M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger–Gromoll metric and a compatible almost complex structure which confers a structure of locally conformal almost K?hlerian manifold to T(M) together with the metric. This is the natural generalization of the well known almost K?hlerian structure on T(M). We found conditions under which T(M) is almost K?hlerian, locally conformal K?hlerian or K?hlerian or when T(M) has constant sectional curvature or constant scalar curvature. Then we will restrict to the unit tangent bundle and we find an isometry with the tangent sphere bundle (not necessary unitary) endowed with the restriction of the Sasaki metric from T(M). Moreover, we found that this map preserves also the natural contact structures obtained from the almost Hermitian ambient structures on the unit tangent bundle and the tangent sphere bundle, respectively. This work was also partially supported by Grant CEEX 5883/2006–2008, ANCS, Romania.     

Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds

In this paper, the author solves the Dirichlet problem for Hermitian-Poisson metric equation √?1Λ_ωG_H = λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds. When λ = 0, the HermitianPoisson metric is a Hermitian harmonic metric.     

Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold

To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski–Sekizawa; in the skew-symmetric one, it does with that obtained by Janyka.