Motion and Special Relativity in Complex Spaces

A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M4 model for special relativity (SR) to complex C4 space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C4 one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M4 real space-time can be recovered. This means all the SR theory is preserved in the real subspace M4 of the space-time C4 while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C4 model to the C3 “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C3 alone. On the other hand, the complex time defined within the C3 theory is interpreted and modeled by the single separate C1 complex plane. The possibility for application of the C3 model to quantum mechanics is suggested. As such, the model C3 seems to have unifying abilities for application to different physical theories.

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.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

An experimental study on fire characteristics of urban complex underground space based on BIM

Compared with the space on the ground,if there is a fire in the urban complex underground space,the loss will be greatly harmful.In addition,the complex underground space is usually connected with other large space areas and densely populated.Once a fire occurs in the complex underground space,it will cause huge property losses and casualties.In order to reduce the risk of fire,it is necessary to deeply understand the development rules and characteristics of fire in the complex underground space of the city.This article has mainly carried on the following work:(I)A particularly complex model of the multi‐storey subway station was built.On this basis,three groups of comparative experiments were conducted to study the effects of fire power,fire location and smoke control system on fire development,and the conclusion that fire location is the most important factor for fire development was obtained;(II)In order to explore the entire space fire and the local space fire,CFD(Computational Fluid Dynamics)is used to build a large‐size fire model and a small‐size fire model respectively;(III)Multiple detector data as temperature slices were built,and it is expected to make full use of the simulation data to deduce the important index of fire location in the early stage of fire.All of the works in this paper will provide reference experimental data for the prevention and firefighting of a sudden fire in the complex underground space.

基于CiteSpace的商业综合体公共空间研究现状综述

随着城市化进程的不断推进,城市居民生活逐渐由物质层面向精神层面延伸。为满足城市商业发展和消费者对商业空间的多元化需求,商业综合体公共空间研究成为重要方面。文章基于中国知网(CNKI)数据库,整理相关文献,运用CiteSpace知识图谱量化文献计量软件,总结2005—2023年该领域发文量变化、关键词及聚类图谱等要素,对该领域的研究趋势进行分析,以期为商业综合体公共空间设计提供参考。

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.

Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space

This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.

B-Implicit Contractive Conditions and Unique（Common） Fixed Points on Complex Valued Metric Spaces

A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.

THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE

In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwahl frame. The geometry of such manifolds is controlled by three real invari- ants which live on T＇M： two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular into, rest. Complex Berwald spaces coincide with K/ihler spaces, in the two - dimensional case, We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kghler purely Hermitian spaces by the fact K = W=constant and I = 0. For the class of complex Berwald spaces we have K =W = 0. Finally, a classitication of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained.

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.

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.

The influence of pore structure on P-& S-wave velocities in complex carbonate reservoirs with secondary storage space

Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin,which is taken as a study case in this paper.It is still not clear how the secondary storage space shape influences the P-＆ S-wave velocities （or elastic properties） in complex carbonate reservoirs.In this paper,three classical rock physics models （Wyllie timeaverage equation,Gassmann equation and the Kuster-Toks z model） are comparably analyzed for their construction principles and actual velocity prediction results,aiming at determining the most favourable rock physics model to consider the influence of secondary storage space shape.Then relationships between the P-＆ S-wave velocities in carbonate reservoirs and geometric shapes of secondary storage spaces are discussed from different aspects based on actual well data by employing the favourable rock physics model.To explain the influence of secondary storage space shape on V P-V S relationship,it is analyzed for the differences of S-wave velocities between derived from common empirical relationships （including Castagna＇s mud rock line and Greenberg-Castagna V P-V S relationship） and predicted by the rock physics model.We advocate that V P-V S relationship for complex carbonate reservoirs should be built for different storage space types.For the carbonate reservoirs in the Tarim Basin,the V P-V S relationships for fractured,fractured-cavernous,and fractured-hole-vuggy reservoirs are respectively built on the basis of velocity prediction and secondary storage space type determination.Through the discussion above,it is expected that the velocity prediction and the V P-V S relationships for complex carbonate reservoirs should fully consider the influence of secondary storage space shape,thus providing more reasonable constraints for prestack inversion,further building a foundation for realizing carbonate reservoir prediction and fluid prediction.

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.

A Characterization of Complex Projective Spaces by Sections of Line Bundles

Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.

A Note on Totally Real Riemannian Foliations with Parallelized Mean Curvature Vectors in a Complex Projective Space

我们讨论了有平行的生叶意味着的完全真实的 Riemannian 在一个复杂射影的空格的弯曲。我们在它上执行了一块向量地的分叉并且获得了西蒙的类型的一个公式。