Abstract
The aim of this paper is to utilize some geometric properties of the de Sitter kinematical group to specify the nature of the potential function $$V\left( x^i\right) $$ intrinsic to the Klein–Gordon equation. For this purpose, in n-dimensional space, the existence of $$(n-1)-$$ and $$n-$$ dimensional subalgebras are necessary to establish the functional forms of the potential function and study its invariant solutions. We demonstrate the use of other group features to construct other potentials of interest. The results are schematicaly displayed in tables.
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