hypercomplex structure
Recently Published Documents


TOTAL DOCUMENTS

7
(FIVE YEARS 0)

H-INDEX

2
(FIVE YEARS 0)

Author(s):  
Mona Atashafrouz ◽  
Behzad Najafi ◽  
Laurian-Ioan Piscoran

Let $G$ be a 4-dimensional Lie group with an invariant para-hypercomplex structure and let $F= \beta+ a\alpha+\beta^2/{\alpha}$ be a left invariant $(\alpha,\beta)$-metric, where $\alpha$ is a Riemannian metric and $\beta$ is a 1-form on $G$, and $a$ is a real number. We prove that the flag curvature of $F$ with parallel 1-form $\beta$ is non-positive, except in Case 2, in which $F$ admits both negative and positive flag curvature. Then, we determine all geodesic vectors of $(G,F)$.  



Author(s):  
Hristo Manev

We study almost hypercomplex structure with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. All the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on one parameter are investigated. There are studied some geometrical characteristics of the respective almost hypercomplex manifolds with Hermitian-Norden metrics.



2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ji Eun Kim ◽  
Su Jin Lim ◽  
Kwang Ho Shon

We define a new hypercomplex structure ofℝ3and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy-Riemann equations in hypercomplex structures ofℝ3.



2010 ◽  
Vol 40 (5) ◽  
pp. 1391-1439 ◽  
Author(s):  
Novica Blažić ◽  
Srdjan Vukmirović


2009 ◽  
Vol 06 (04) ◽  
pp. 619-624 ◽  
Author(s):  
HAMID REZA SALIMI MOGHADDAM

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi–Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have constant scalar curvature. We also show that they are flat or they have only non-negative or non-positive sectional curvature.



2000 ◽  
Vol 11 (07) ◽  
pp. 925-942 ◽  
Author(s):  
LIVIU ORNEA ◽  
PAOLO PICCINNI

We describe a diagram containing the zero sets of the moment maps associated to the diagonal U(1) and Sp(1) actions on the quaternionic projective space ℍPn. These sets are related both to focal sets of submanifolds and to Sasakian–Einstein structures on induced Hopf bundles. As an application, we construct a complex structure on the Stiefel manifolds [Formula: see text] and [Formula: see text], the one on the former manifold not being compatible with its known hypercomplex structure.



Sign in / Sign up

Export Citation Format

Share Document