Topologically knotted Lagrangians in simply connected four-manifolds

Vidussi was the first to construct knotted Lagrangian tori in simply connected four-dimensional manifolds. Fintushel and Stern introduced a second way to detect such knotting. This note demonstrates that similar examples may be distinguished by the fundamental group of the exterior.

     

Differential geometry of tensor product immersions

In this article we obtain the best possible estimates of the type number of tensor product immersions and investigate tensor product immersions with lowest possible type. Several classification theorems in this respect are then proved.     

固体样品进样技术中汞量定标方法的研究

在原子吸收光谱分析中,固体样品直接进样是目前的研究课题之一。本文主要报道作者在分析汞中所进行的固体直接进样技术工作和讨论。在我们研制成功的KT—81型塞曼效应测汞仪中,针对元素汞蒸气压高的特点,用饱和汞蒸气作为汞量标准,实现了固体样品,如土壤、污泥、毛发、煤、食品等汞含量的直接进样测定。汞蒸气一次制备后可长期使用。分析汞时,只要用标准气体任意校验一次就可测量。1～2分钟能分析一个样品,S<0.3ng。r<5%。此法用NBS标准物质验证过。     

Codimension reduction in symmetric spaces

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.     

复射影空间CP~((n+p)/2)中具有2-调和的一般子流形

本文研究了复射影空间中具有2-调和的一般子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的Pinching定理和Simons型积分不等式,此外还得到关于2-调和伪脐一般子流形的一个刚性定理,推广了复射影空间中具有2-调和全实子流形的一些相应结果.     

A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group ${\text{Nil}}_3$, the universal covering of the Lie group $\text{PSL}(2,\mathbb{R})$ and the Lie group ${\text{Sol}}_3$) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.     

A generalized preimage theorem in global analysis

The concept of locally fine point and generalized regular value of a C¹ map between Banach spaces were carried over C¹ map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.     

Loop Groups and Twin Buildings

In these notes we describe some buildings related to complex Kac–Moody groups. First we describe the spherical building of SL_n() (i.e. the projective geometry PG(ⁿ)) and its Veronese representation. Next we recall the construction of the affine building associated to a discrete valuation on the rational function field (z). Then we describe the same building in terms of complex Laurent polynomials, and introduce the Veronese representation, which is an equivariant embedding of the building into an affine Kac–Moody algebra. Next, we introduce topological twin buildings. These buildings can be used for a proof which is a variant of the proof by Quillen and Mitchell, of Bott periodicity which uses only topological geometry. At the end we indicate very briefly that the whole process works also for affine real almost split Kac–Moody groups.Supported by a Heisenberg fellowship by the Deutsche Forschungsgemeinschaft.