COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

在复二维仿射锥上的完备余齐性一Kahler度量

In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.

Kahler流形上有关Bakry-Emery曲率的Schur引理（英文）

本文研究了K(a|¨)hler流形上有关Bakry-Emery曲率的Schur引理.即在K(a|¨)hler流形上考虑方程R_(ij)+f_(ij)=λg_(ij),其中f,λ是光滑实值函数.利用Bianchi恒等式,得到了λ是常数.

Tensor-Centric Warfare IV:Kahler Dynamics of Battlefields

This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW;for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lanchester-type combat equations, entropic Lie-dragging and commutators for modeling warfare uncertainty and symmetry, and various delta-strikes and missiles (both deterministic and random). The present paper gives a unique synthesis of the Red vs. Blue vectorfields into a single complex battle-vectorfield, using dynamics on Kähler manifolds as a rigorous framework for extending the TCW concept. The global Kähler dynamics framework, with its rigorous underpinning called the Kähler-Ricci flow, provides not only a new insight into the “geometry of warfare”, but also into the “physics of warfare”, in terms of Lagrangian and Hamiltonian structures of the battlefields. It also provides a convenient and efficient computational framework for entropic wargaming.

The Equivalence between Bergman Metric and Einstein-Kahler Metric on the Cartan-Hartogs Domain of the Fourth Type

In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Khler metric on the Cartan-Hartogs domain of the fourth type.

C^(3)中曲面Kahler角的刚性定理（英文）

浸入到近复Hermit流形的曲面的Khler角是一个重要的不变量,可以用于刻画曲面偏离拟全纯曲线的程度.近年来,具有常Khler角的曲面仍是很有意义的研究对象.对于3维复欧氏空间C^3中具有常Khler角的曲面收缩子,本文证明了两个刚性定理.这些定理是有关C^3中曲面自收缩子的相应定理的直接拓展.

一类Reinhardt域的群不变函数与不变Kahler度量

本文把［１］的结果推广到更广泛的一类Ｒｅｉｎｈａｒｄｔ域Ｄ＝Ｄ（ｋ１ｋ２…ｋｐ） Ｃ（１≤ｐ＜ｎ），即利用Ｄ的解析自同构群Ａｕｔ（Ｄ）下不变函数给出了域Ｄ在Ａｕｔ（Ｄ）下不变的Ｋａｈｌｅｒ度量．

HAMILTONIAN MECHANICS ON KAHLER MANIFOLDS

Using the mechanical principle, the theory of modern geometry and advanced calculus, Hamiltonian mechanics was generalized to Kahler manifolds, and the Hamiltonian mechanics on Kahler manifolds was established. Then the complex mathematical aspect of Hamiltonian vector field and Hamilton＇s equations was obtained, and so on.

INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD

The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential

LAGRANGIAN MECHANICS ON KAHLER MANIFOLDS

Lagrangian mechanics on Kahler manifolds were discussed, and the complex mathematical aspects of Lagrangian operator, Lagrange＇s equation, the action functional, Hamilton＇ s principle, Hamilton＇ s equation and so on were given.

ON MINIMAL IMMERSIONS OF R^2 INTO THE NEARLY KAHLER S^6

In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.

One Nonparabolic End Theorem on Kahler Manifolds

In this paper, the complete noncompact Kahler manifolds satisfying the weighted Poincare inequality are considered and one nonparabolic end theorem which generalizes Munteanu＇s result is obtained.

Kahler’s Disease with a Rare Clinical form and Review of Literature

Kahler’s disease or “multiple myeloma” is a cancerous disease of the bone marrow. It may appear straightaway in its multiple myeloma form or in the form of solitary bone plasmacytoma or extra bone plasmacytoma. In the extra bone form, its orbital location as the first symptom is exceptional. Our case concerned a 49-year-old female patient without significant medical history who was followed for 6 months for a voluminous left exophthalmos. This ocular symptomatology was accompanied six months after by acute bone pains in the spine and pelvis then by a pathological fracture of the left trochanter. Histological assessment during the treatment showed the diagnosis of Kahler’s disease. The serum calcium was 106 mmol/l, a blood level of chloride to 96 mmol/l, of potassium to 5.36 mmol/l, of sodium to 136 mmol/l. The 24-hour proteinuria was 0.30 g/l and indicated renal impairment. The patient had anemia with a hemoglobin level to 8.8 g/l. Tumor markers were normal;in particular the CA was 13.148, ACE-2 to 1.013 ng/ml and CA19-9 to 5.029 IU/ml. The patient was transferred to a specialized unit but died before the start of treatment. Thus any isolated exophthalmos or accompanied by bone signs must systematically suggest Kahler’s disease and make undertake investigations in this direction. It is on this condition that an early management of the disease can improve the prognosis of the disease and prolong the patient’s life.

NEWTONIAN MECHANICS ON KAHLER MANIFOLD

In this paper we discuss Newtonian Mechanics on Kahler Manifold, and also givefoe complex mathematical aspects of Newton's law, the law of kinetic energy, the lawof kinetic quantity,the equation of motion and the 'general equation of dynamics',and so on.

Nearly para-Kahler流形H_(3)^(6)上的殆仿切触拉格朗日子流形

给出nearly para-Kahler流形H3^6的一个拉格朗日子流形M上的一个单位向量场ξ典范引出的殆仿切触度量结构是quasi-para-Sasakian,α-para-Kenmotsu的充要条件.同时推导出当M上典范诱导的仿切触度量结构是para-Sasakian的一个必要条件.

关于Kahler流形上的Newton力学

本文讨论Ｋａｈｌｅｒ流形上的Ｎｅｗｔｏｎ力学．在此给出Ｎｅｗｔｏｎ定律、动能定律、动量定律、虚位移原理、Ｄ＇Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理、运动方程及“普遍运动方程”等的复的数学形式．

李奇曲率平行的Kahler流形的孤立现象

证明了李奇曲率平行的Ｋａｈｌｅｒ流形上的黎曼曲率的Ｐｉｎｃｈｉｎｇ定理。

S^6中具有常数Kahler角的极小曲面

球面Ｓ６具有典型的近复结构，因而对于其中的曲面可引入Ｋａｈｌｅｒ角的概念．本文研究Ｓ６内具有常数Ｋａｈｌｅｒ角的极小曲面，得到了刚性定理．结合已有结果，易知Ｓｉｍｏｎ猜想对于这类曲面成立．

紧致局部共形Kahler流形上Morse-Novikov上同调群的一个关系

利用谱序列方法,作者证明了紧致局部共形Khler流形上关于Morse-Novikov上同调群的一个关系,这个关系可以看作一般紧致复流形上Frlicher关系的类比.同时,作者证明了在维数大于2的对角Hopf流形上存在局部共形Khler结构,使得其Morse-Novikov上同调群分别满足对称性和直和性.

关于紧致近p-Kahler流形的全纯形变开性

在本文中,我们在n维紧致复流形X上定义了近p-Khler度量,即考虑紧致复流形X上的Hermitian度量h,它的Hermitian形式ω满足如下近p-Khler条件:d(ωp+σ)=0,其中1≤p≤n-1是整数,σ是实(p,p)-形式(这里σ≠-ωp).我们称h为近p-Khler度量.我们证明了在假定(n-1,n)-弱-引理性质和(n-1,n-1)-Hermitian性质成立的前提下,近(n-1)-Khler度量是全纯形变开的.