SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY

A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.

RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS

We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Space Forms

Let M be a real hypersurface of a complex space form with almost contact metric structure (φ,ξ,η,g). In this paper, we prove that if the structure Jacobi operator Rξ=(·,ξ) ξ is φ▽ξξ-parallel and Rξ commute with the shape operator, then M is a Hopf hypersurface. Further, if Rξ is φ▽ξξ-parallel and Rξ commute with the Ricci tensor, then M is also a Hopf hypersurface provided that TrRξ is constant.

Classification of Lagrangian Surfaces of Curvatureε in Non-fiat Lorentzian Complex Space Form ■_1~2(4ε)

It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.

Conformally flat, minimal, Lagrangian submanifolds in complex space forms

We investigate n-dimensional(n≥4),conformally flat,minimal,Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those that admit at most one eigenvalue of multiplicity one.In the case where the ambient space is Cn,the quasi umbilical case was studied in Blair(2007).However,the classification there is not complete and several examples are missing.Here,we complete(and extend) the classification and we also deal with the case where the ambient complex space form has non-vanishing holomorphic sectional curvature.

Ruled Real Hypersurfaces of A Complex Space Form

The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.

2-Harmonic Submanifolds in a Complex Space Form

In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.

Lagrangian Bonnet Problems in Complex Space Forms

In this note we consider Lagrangian Bonnet problem for Lagrangian surfaces in complex space forms. We first give a Bonnet type theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface with the same mean curvature form, unless the Maslov form is conformal. These two Lagrangian surfaces are then called Lagrangian Bonnet pairs. We also studied Lagrangian Bonnet surfaces in complex space forms, and obtain some characterizations of such surfaces.

ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS

New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.

商业综合体周边人行尺度风环境模拟优化

商业综合体有利于促进产业集聚化和功能复合化,在城市中具有特殊的区位价值和高度整合的功能。如何充分发挥商业综合体对城市空间的结构引导作用,打造绿色生态城市空间,成为亟待解决的问题。文章以建筑周边人行感受为出发点,对商业综合体周边人行高度风环境进行系统分析。利用Butterfly软件,对不同商业综合体总体布局的各风环境指数进行了整理和比较,以研究不同布置模型下能否提供更佳的城市及人行风环境设计策略,从而提供对商业综合体建筑形态与建筑布局方向的设计策略。

拆模工序对沈阳文化艺术中心音乐厅缓黏结预应力结构内力变形的影响

为了探明模架拆除对复杂大空间大悬挑结构内力及变形的影响,对沈阳文化艺术中心音乐厅结构进行施工阶段有限元分析。在分析中,考虑了混凝土、钢束等材料的时效性能,利用"生死技术"设计了4个拆模阶段、6种拆模方案,考察各拆模方案、拆模阶段对音乐厅结构变形、关键构件的混凝土及钢束的应力分布。分析结果表明:1虽然各方案模架拆除顺序不同,但最终状态下音乐厅的变形最大位移均出现在屋顶悬挑端部;2当拆除23.2 m悬挑区域模架时,对音乐厅结构的变形变化、混凝土应力分布以及钢束有效应力变化具有较大影响;3当拆除屋顶非悬挑区域模架时,方案一、方案三和方案五音乐厅悬挑端均出现向上翘曲的变形;4建议采用二、四或六拆模方案进行施工。

一类不定复空间型中Lagrange子流形的Chen型不等式

利用Riemann不变量和Riemann流形上的最优化方法得到一类不定复空间型中Lagrange子流形的Chen型不等式,并证明了等号成立时子流形一定为全测地的.

复空间形式中具有常数量曲率的全实子流形(英文)

本文研究了复空间形式中具有常数量曲率的全实子流形.利用一种自伴算子,得到了这类子流形关于第二基本形式模长平方的积分不等式.

容有半对称度量联络的广义复空间中子流形上的Chen不等式（英文）

在容有半对称度量联络的广义复空间中建立了子流形上的Chen不等式,这些不等式给出了子流形的平均曲率(关于半对称联络)与截面曲率,数量曲率之间的关系.

空间基因的内涵与作用机制

空间基因承载着“城市空间-自然环境-社会人文”互动演化模式的空间信息,在城市空间文脉传承中起着关键性作用。一直以来,以建成环境遗产保护、符号复制或形态模仿方式进行的城市文脉传承,忽视了对空间基因的关注,导致即使存“物”,也失“脉”。因此,在城市研究中运用空间基因理论,深入理解空间基因的内涵与作用机制十分必要。城市空间形态(性状)的发展规律可以运用“空间基因”解释:通过“变异”与“选择”,生成空间基因这一地域性空间组合模式,从而决定城市空间的某些性状;然后,通过“编码”“复制”与“表达”,实现城市空间文脉的传承。“空间基因”研究可以使城市历史文脉保护与规划设计方法产生方向性转变,使其从感性的空间形式模仿或创作,走向理性的空间建构规则分析,是修正当前对城市空间发展错误认知、改进规划设计策略与方法的重要基础。

伪复空型的分解与分类

主要研究具有平行ｆ─结构的伪复空型的分解及分类问题。

复空间形式的紧致全实伪脐子流形

主要研究复空间形式中具有平行法平均曲率向量的紧致全实伪脐子流形,给出了截面曲率作为全脐子流形判定条件的结果.

双相复空型及其几何特征

定义了一类特殊的Bochner-Kachler流形——双相复空型,讨论它的曲率张量表达式和一些几何特征,并给出了具体例子.

一种复杂曲面型遮光罩的成型技术

随着空间遥感技术的发展,遮光罩的结构形式也变得更加复杂和多样化。百叶罩是近年来出现的一种复杂曲面型空间遥感器遮光罩。在方案阶段,曾采用传统的金属材料制造百叶罩,但存在机械加工困难、尺寸精度低、振动试验受损等一系列技术问题。文章介绍了一种芳纶纤维增强树脂基复合材料百叶罩的成型技术,重点对材料选择、工艺方案、模具设计、铺叠方法等内容进行了讨论。研究结果表明:基于周向抱合式组合模具,采用一体化成型方法,能够实现类似复杂曲面型遮光罩的精密成型,产品具有较高的尺寸精度及力学性能,并满足空间遥感器系统的使用要求。

复空间形式的紧致全实伪脐子流形

研究了复空间形式中具有平行法平均曲率向量的紧致全实伪脐子流形.给出了R icc i曲率成为全脐子流形的判定条件.