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Let $G$ be a connected Lie group of rank one. In this paper the existence offree actions of group $G$ on spheres, real projective spaces and lens spaceshas been studied. Most of the results have been obtained for finitistic spaceswith cohomology ring isomorphic to the cohomology ring of these spaces. Thecohomology algebra of the orbit space has been determined in the case of free$G$-action. The non-existence of $G$-equivariant maps from spheres tocohomology spheres has also been established.

Free actions of connected Lie groups of rank one on certain spaces