Quaternion functions and four-dimensional Riemannian metrics
Data de publicação2005-01-01
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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. © Dynamic Publishers, Inc.