INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD

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

ON PSEUDO-HOLOMORPHIC CURVES IN COMPLEX GRASSMANNIANS

0.IntroductionAsiswellknown,beginingwithaharmonicmapf:M-Gm(C")fromaRiemannstirfacetoacomplexGrassmannian,onecanobtaintheharmonicsequencesbyusingthe0-transformand0--transform.[1]Whenfisholomorphic,eachelementintheharmonicscsquenceiscalledapseudo-holomorphiccurveandthecorespondingmapiscalledapseudosholomorphicmap.[2]Theimportanceofsuchmapscomesfromthefactthatanyharmonicmapgb:M-- CPu~GI(C" ')ispseudo-holomorphicifIdeg(rk)I>n(g--1)wheredeg(rk)isthedegreeofacandgisthegenusofM.13'4]In[5]J.Bol…     

Real Hypersurfaces in Complex Two-Plane Grassmannians

 The complex two-plane Grassmannian G ₂(C ^m+2 in equipped with both a K?hler and a quaternionic K?hler structure. By applying these two structures to the normal bundle of a real hypersurface M in G ₂(C ^m+2 one gets a one- and a three-dimensional distribution on M. We classify all real hypersurfaces M in G ₂ C ^m+2 , m≥3, for which these two distributions are invariant under the shape operator of M. Received 13 November 1996; in revised form 3 March 1997     

On Some Properties of the Quaternionic Functional Calculus

In some recent works we have developed a new functional calculus for bounded and unbounded quaternionic operators acting on a quaternionic Banach space. That functional calculus is based on the theory of slice regular functions and on a Cauchy formula which holds for particular domains where the admissible functions have power series expansions. In this paper, we use a new version of the Cauchy formula with slice regular kernel to extend the validity of the quaternionic functional calculus to functions defined on more general domains. Moreover, we show some of the algebraic properties of the quaternionic functional calculus such as the S-spectral radius theorem and the S-spectral mapping theorem. Our functional calculus is also a natural tool to define the semigroup e ^tA when A is a linear quaternionic operator.      

社会整体性的表征：卡勒“理论”的生产性

关于“理论”,乔纳森·卡勒做过若干界定,解释性是其特性之一。“理论”的反思性、批判性恰恰是通过其解释性而实现的。在卡勒那里,文化研究与“理论”是两个可以相互置换的概念。这两者产生于文学研究但却挤压和排斥了文学研究,从而实现了方法论的转变,将文学解释为社会整体性的表征。于是对文学对象的阅读就有了诗学模式/解释学模式、恢复解释学/怀疑解释学、表征性解释/症候性解释等一系列不同类型、不同层次的区分。本文通过对于这些错综复杂、欲理还乱的关系的厘定和归置,揭示了“理论”作为一种人文学科的新文类,具有显著的观念生产、知识增长和学术建构的功效。     

L2-harmonic 1-forms on Complete Manifolds

We study the global behavior of complete minimal δ-stable hypersurfaces in R~(n+1) by using L~2-harmonic 1-forms.We show that a complete minimal δ-stable(δ (n-1)~2/n~2)hypersurface in R~(n+1) has only one end.We also obtain two vanishing theorems of complete noncompact quaternionic manifolds satisfying the weighted Poincar′e inequality.These results are improvements of the first author's theorems on hypersurfaces and quaternionic K¨ahler manifolds.     

Quaternionic triangular linear operators

Triangular operators are an essential tool in the study of nonselfadjoint operators that appear in different fields with a wide range of applications. Although the development of a quaternionic counterpart for this theory started at the beginning of this century, the lack of a proper spectral theory combined with problems caused by the underlying noncommutative structure prevented its real development for a long time. In this paper, we give criteria for a quaternionic linear operator to have a triangular representation, namely, under which conditions such operators can be represented as a sum of a diagonal operator with a Volterra operator. To this effect, we investigate quaternionic Volterra operators based on the quaternionic spectral theory arising from the S-spectrum. This allow us to obtain conditions when a non-selfadjoint operator admits a triangular representation.     

K(a)hler流形上的不变形式和积分不变量

用现代微分几何理论和高等微积分把Poincare和Cartan-Poincare积分不变量的晕要思想和结果以及E．Cartan在经典力学中首先建立的积分不变量和不变形式的关系推广到Kahler流形上的Hamilton力学中去，得到相应的更广泛的结果．     

Weyl Connections and Curvature Properties of CR Manifolds

We announce the existence of metrics of positive sectional curvature onthe 3-Sasakian reductions of S¹¹ by an isometric circleaction.     

Hyper-Hermitian Quaternionic Kähler Manifolds

We call a quaternionic Kähler manifold with nonzero scalar curvature, whosequaternionic structure is trivialized by a hypercomplex structure, ahyper-Hermitian quaternionic Kähler manifold. We prove that every locallysymmetric hyper-Hermitian quaternionic Kähler manifold is locally isometricto the quaternionic projective space or to the quaternionic hyperbolic space.We describe locally the hyper-Hermitian quaternionic Kähler manifolds withclosed Lee form and show that the only complete simply connected suchmanifold is the quaternionic hyperbolic space.