<Emphasis Type="Italic">N</Emphasis> = 4 supersymmetric Eguchi-Hanson sigma model in <Emphasis Type="Italic">d</Emphasis> = 1

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi-Hanson target space is investigated in detail: we present the standard and quotient approaches to get the Eguchi-Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Local Schrodinger flow into Kahler manifolds

In this paper we show that there exists a unique local smooth solution for the Cauchy problem of the Schrodinger flow for maps from a compact Riemannian manifold into a complete Kahler manifold, or from a Euclidean space Rm into a compact Kahler manifold. As a consequence, we prove that Heisenberg spin system is locally well-posed in the appropriate Sobolev spaces.     

关于球面到CPN中的共形极小浸入

本文证明一个关于球面Ｓ~２ 到ＣＰ~Ｎ中的共形极小浸入的曲率ｐｉｎｃｈｉｎｇ定理．     

关于球面到CPN中的共形极小浸入

本文证明一个关于球面Ｓ² 到ＣＰ^N中的共形极小浸入的曲率ｐｉｎｃｈｉｎｇ定理．     

Maximal holonomy of infra-nilmanifolds with -dimensional quaternionic Heisenberg geometry

Let be the quaternionic Heisenberg group of real dimension and let denote the maximal order of the holonomy groups of all infra-nilmanifolds with -geometry. We prove that . As an application, by applying Kim and Parker's result, we obtain that the minimum volume of a -dimensional quaternionic hyperbolic manifold with cusps is at least

     

Generalized holomorphic orthogonal function systems over infinite cylinders

In this paper we construct two distinct generalized holomorphic orthogonal function systems over infinite cylinders in . Explicit representation formulae and properties of the obtained basis functions are given. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2014 John Wiley & Sons, Ltd.     

四元Heisenberg群上的一个半线性问题

本文研究了四元Heisenberg群上的一个半线性方程问题,通过把对应的方程问题化为积分进行估计,证明了其对应的半线性方程的非负双椭圆解只有唯一的零解,推广了相应Heisenberg群上的定理.     

A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector-valued function

In this paper, we combine the fractional $\psi -$hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel–Pompeiu type formula related to a fractional $\psi -$Fueter operator with respect to a vector-valued function is proved.