反常霍尔效应理论的研究进展

文章介绍了在铁磁性材料中反常霍尔效应的发现及其机制研究的历史；阐述了反常霍尔效应理论研究最近取得的重大进展，即倒空间中布洛赫态的贝里曲率（规范场）特性决定了霍尔电导率；同时指出，建立系统地解释反常霍尔效应机制的理论仍然是一个挑战性的任务．     

Quantum fluctuations of vacuum stress tensors and spacetime curvatures

We analyze the quantum fluctuations of vacuum stress tensors and spacetime curvatures, using the framework of linear response theory which connects these fluctuations to dissipation mechanisms arising when stress tensors and spacetime metric are coupled. Vacuum fluctuations of spacetime curvatures are shown to be a sum of two contributions at lowest orders; the first one corresponds to vacuum gravitational waves and is restricted to light-like wavevectors and vanishing Einstein curvature, while the second one arises from gravity of vacuum stress tensors. From these fluctuations, we deduce noise spectra for geodesic deviations registered by probe fields which determine ultimate limits in length or time measurements. In particular, a relation between noise spectra characterizing spacetime fluctuations and the number of massless neutrino fields is obtained.     

Total curvatures of compact complex submanifolds inC/P^n

LetM be a complex submanifold in . We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in .Partially supported by Fundació Caixa Castelló grant n. MI25043/92.Partially supported by the Spanish DGICYT grant #PB91 — 0324.     

Ricci Collineations in Perfect Fluid Bianchi V Spacetime

The Bianchi V spacetimes with perfect-fluid matter are classified according to their Ricci collineations. We have found that in the degenerate case there are infinitely many Ricci collineations whereas a subcase gives a finite number of Ricci collineations which are five. In the non-degenerate case the group of Ricci collineations is finite, i.e. four or five or six or seven. Also, all results obtained satisfy the energy conditions.     

anti-de Sitter 空间中紧致类空超曲面的积分公式及其在常高阶平均曲率下的应用

该文对 anti-de Sitter 空间H₁ⁿ⁺¹中的紧致类空超曲面建立了积分公式,并应用它们在常高阶平均曲率的条件下讨论了H₁ⁿ⁺¹中紧致类空超曲面的全脐问题.     

Characterizing horospheres of the hyperbolic space via higher order mean curvatures

In this paper we establish new characterization results concerning horospheres of the hyperbolic space under certain appropriate constraints in the behavior of the higher order mean curvatures. Our approach is based on a suitable maximum principle for complete Riemannian manifolds. Moreover, we present examples showing the importance of the main hypothesis of our results.     

曲率的形状梯度和经典梯度:微纳米曲面上的驱动力

近期的实验和分子动力学模拟均表明:圆锥面上粘附液滴能自发地定向运动,且自发定向运动的方向与粘附面的亲水、疏水性质无关．针对这一重要现象,拟从曲面微纳米力学几何化的角度,提供一般性的理论解释．借助于粒子对势,研究了孤立粒子与微纳米硬曲面之间的相互作用,分析了粒子/硬曲面相互作用的几何学基础．可以证实:（a） 粒子/硬曲面的作用势均具有统一的曲率化形式,均可以统一地表达成曲面平均曲率和Gauss曲率的函数;（b） 基于曲率化的作用势,能够实现曲面微纳米力学的几何化;（c） 曲率与曲率的内蕴梯度构成卷曲空间上的驱动力;（d） 驱动力方向与曲面的亲水、疏水性质无关,解释了自发定向运动实验．     

Conditions for the occurence of strong curvature singularities

Necessary and sufficient conditions for the occurrence of strong curvature singularities as defined by Tipler and Królak are derived. It is shown that both necessary and sufficient conditions involve not only the divergence of tetrad components of the Riemann, Ricci or Weyl tensor but also the divergence of their integrals along nonspacelike geodesics running into the singularity.