The purpose of this paper is to study n-dimensional QRsubmanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form and to classify such submanifolds under certain conditions concerning the second fundamental form and the induced almost contact 3-structure. M.S.C. 2010: 53C40, 53C25.

Quaternionic linear algebra and plurisubharmonic functions of quaternionic variables. Abstract We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. The main point of this paper is that in quaternionic algebra and analys...

In this paper, we give an analogue of Jørgensen’s inequality for non-elementary groups of isometries of quaternionic hyperbolic space generated by two elements, one of which is elliptic. As an application, we obtain an analogue of Jørgensen’s inequality in 2-dimensional Möbius group of the above case. 2000 Mathematics subject classification: primary 30F40; secondary 20H10, 57S30.

Motivated by the analogies between the projective and the almost quaternionic geometries, we first study the generalized planar curves and mappings. We follow, recover, and extend the classical approach, see e.g. [9, 10]. Then we exploit the impact of the general results in the almost quaternionic geometry. In particular we show, that the natural class of H–planar curves coincides with the clas...