Finitely generated gyrovector subspaces in the Möbius gyrovector space (Researches on isometries from various viewpoints)

Abstract

We show that any finitely generated gyrovector subspace in the Möbius gyrovector space coincides with the intersection of the linear subspace generated by the same generators and the Möbius ball. As an application, we present a notion of orthogonal gyrodecomposition and clarify the relationship with the orthogonal decomposition. In addition, an announce of the abstract of the results which were recently obtained by the second author will be made. One of the main results is the orthogonal gyroexpansion of an arbitrary element with respect to any orthogonal basis in the Möbius gyrovector space and its concrete procedure to calculate the gyrocoefficients.