QUATERNION FUNCTIONS AND FOUR-DIMENSIONAL RIEMANNIAN METRICS

TitleQUATERNION FUNCTIONS AND FOUR-DIMENSIONAL RIEMANNIAN METRICS
Publication TypeJournal Article
Year of Publication2005
AuthorsMachado, JM
Secondary AuthorsBorges, MF
Secondary TitleCommunications in Applied Analysis
Volume9
Issue1
Start Page15
Pagination31
Date Published01/2005
Type of Workscientific: mathematics
ISSN 1083–2564
AMS30E99, 30G99
Abstract

In this paper we discuss homeomorphic transformations of Riemannian metrics in four-dimensional  Riemannian manifolds, and show that these transformations are related to the solutions of Beltrami-type systems of differentiable, quaternionic functions. It is introduced the concept of quaternionic factorization of metrics, and demonstrated that monogenic functions are a particular case in a larger class of quaternionic differentiable functions. This class is formed by the solutions of an homogeneous operator equation, constructed for any factorizable, Riemannian metric.

 
URLhttp://www.acadsol.eu/en/articles/9/1/2.pdf
Short TitleQuaternion Functions
Refereed DesignationRefereed
Full Text

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