On the Normality of an Almost Contact 3-Structure on QR-Submanifolds

We study n-dimensional QR-submanifolds of QR-dimension (p – 1) immersed in a quaternionic space form QP ^(n+p)/4(c), c 0, and, in particular, determine such submanifolds with the induced normal almost contact 3-structure.     

A direct approach to quaternionic manifolds

The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on , in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure.     

Relaxed quaternionic Gabor expansions at critical density

Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion‐valued signal f in the Wiener space can be expanded into a unique ? ² series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion . Copyright © 2016 John Wiley & Sons, Ltd.     

四元Heisenberg群上的链和R-圆及其性质

定义了四元双曲空间上的链和R-圆,并给出了链在垂直投影下的性质.证明了经过Heisenberg群上固定两点的链的唯一性,R-球的qc-水平性,并给出了R-圆与纯虚R-圆之间的关系.     

ON THE KAHLER-RICCI SOLITONS WITH VANISHING BOCHNER-WEYL TENSOR＊

In this article,we study the steady,shrinking,and expanding K(a)hler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that,under this condition,the Ricci solitons must have constant holomorp...     

三维Minkowski空间中的极小曲面

给出了三维Minkowski空间中类空曲面活动标价的四元素表示,并利用四元素既适合于旋转结构的侵入又适合于2×2矩阵处理极小曲面的分析特性,经研究得到了R12中的极小曲面Weierstrass表示和曲面的可积条件.     

Characterizing Specific Riemannian Manifolds by Differential Equations

Some characterizations of certain rank-one symmetric Riemannian manifolds by the existence of nontrivial solutions to certain partial differential equations on Riemannian manifolds are surveyed.     

On uniform estimate in Calabi-Yau theorem

We show that the uniform estimate in the Calabi-Yau theorem easily follows from the local stability of the complex Monge-Ampere equation.     

Universality properties of the quaternionic power series and entire functions

In this paper we establish the existence of “almost universal” quaternionic power series and entire functions. Denoting by B(0, 1) the open unit ball in , this means that there exists a quaternionic power series with radius of convergence 1 such that, denoting by the n‐th partial sum of S, for every , for every axially symmetric open subset Ω of containing K and every f slice regular on Ω, there exists a subsequence of the partial sums of S such that uniformly on K, as . The symbol denotes the set of axially symmetric compact sets in such that is connected for some . This is a slightly weaker property than the classical universal power series phenomenon obtained for analytic only on the interior of K and continuous on K. We also generalize a result originally proven by Birkhoff and finally we show that there exists an entire quaternionic function whose set of derivatives is dense in the class of entire quaternionic functions.     

The domain of definition of the quaternionic Monge–Ampère operator

In this paper, we give an equivalent characterization of the domain of definition for the quaternionic Monge–Ampère operator, by using the theory of quaternionic closed positive current we established in [17–19]. This domain of definition for the complex Monge–Ampère operator was introduced by Blocki [7,8].